6th grade - njctl
TRANSCRIPT
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6th Grade
Fraction & Decimal Computation
2015-10-20
www.njctl.org
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Fraction and Decimal Computation
· Long Division Review· Adding Decimals· Subtracting Decimals
Click on the topic to go to that section
· Multiplying Decimals· Dividing Decimals· Glossary & Standards
· Fraction Division
· Distributive Property & Product of Decimals
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Fraction and Decimal Computation
· Long Division Review· Adding Decimals· Subtracting Decimals
Click on the topic to go to that section
· Multiplying Decimals· Dividing Decimals· Glossary & Standards
· Fraction Division
· Distributive Property & Product of Decimals
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Teac
her N
otes Vocabulary Words are bolded
in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
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Fraction Division
Return toTable ofContents
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Modeling DivisionRecall from 5th grade:
When we are dividing, we are breaking apart into equal groups.
The model below represents: 8 ÷ 4 = 2
2 groups of 4
Dividend ÷ Divisor = Quotient
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Applying to FractionsThe previous example used whole numbers and grouped the dividend according to the divisor.
The same strategy can be applied when dividing with fractions.
Use the model below to demonstrate: 8 ÷ =
8
The pink rectangle represents .
See how many you can fit in the 8 squares.
12
12
12
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Applying to FractionsThe previous example used whole numbers and grouped the dividend according to the divisor.
The same strategy can be applied when dividing with fractions.
Use the model below to demonstrate: 8 ÷ =
8
The pink rectangle represents .
See how many you can fit in the 8 squares.
12
12
12
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Teac
her N
otes The "half" square is infinitely
cloned and students should "fill" the 8 squares with 16
half squares to show
8 / 0.5 = 16
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ExampleUse the model below to demonstrate 2 ÷ =
2
13
13
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1 Evaluate the following problem using the model below.
3
14
3 ÷ =
14
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1 Evaluate the following problem using the model below.
3
14
3 ÷ =
14
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12
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2 Evaluate the following problem using the model below.
5
12
5 ÷ =
12
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2 Evaluate the following problem using the model below.
5
12
5 ÷ =
12
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10
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A fraction can be divided by a whole number using the following visual model. 3/5 ÷ 4
Divide into 4 groups
1 2 3 4
Visual Model
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A fraction can be divided by a whole number using the following visual model. 3/5 ÷ 4
Divide into 4 groups
1 2 3 4
Visual Model
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wer
3/5 ÷ 4 = 3/20
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The previous expression can be represented by the following word problem: How much will each person receive if 4 friends share a 3/5 pound bag of popcorn?
1 2 3 4
Each friend will receive 3/20 lb. of popcorn.
Word Problem
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Vocabulary Review
Complex Fraction: A fraction with another fraction in the numerator, denominator or both.
Original Number 4
Reciprocal 2
Reciprocal: The inverse of a number/fraction.
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PatternsDo you notice a pattern between the division of fractions and their solution?
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PatternsDo you notice a pattern between the division of fractions and their solution?
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Teac
her N
otes
Discuss Patterns either from model or number sentence.
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If you think about it, we are dividing by a fraction which creates a complex fraction.
You need to eliminate the fraction in the denominator in order to solve the problem.
To do this, multiply the numerator and denominator of the complex fraction by the reciprocal of the denominator (making the denominator = 1).
You can then simplify the fraction by rewriting it without the denominator of 1 and solve the new multiplication problem.
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source - http://www.helpwithfractions.com/dividing-fractions.html
There are rules that can be applied to fraction division problems to eliminate steps from this lengthy procedure.
1 2
x 3 2
= 1 2
2 3
=
1 2
2 3
=
1 2 2 3
x 3 2
x 3 2
=
1 2
x 3 2
1
OriginalProblem
ComplexFraction
Multiply byReciprocal
SimplifyDenominator
RewriteWithout 1
Example
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Algorithm
Step 1: Leave the first fraction the same.
Step 2: Multiply the first fraction by the reciprocal of the second fraction.
Step 3: Simplify your answer.
Dividing Fractions Algorithm
1 5
x 2 1
= 1 x 2 5 x 1
= 2 5
1 5
1 2
=
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Some people use the saying " Keep Change Flip" to help them remember the algorithm.
3 5
x 8 7
= 3 x 8 5 x 7
= 2435
3 5
7 8
=
KeptChanged
FlippedKeepChange
Flip
Dividing Fractions Algorithm
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Checking Your AnswerTo check your answer, use your knowledge of fact families.
35
78
2435
÷ =
35
= 2435
78
x
35 is 7
8of 24
35
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7 )
True
False
8 10
= 5 4
x 8 10
4 5
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7 )
True
False
8 10
= 5 4
x 8 10
4 5
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FALSE
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8 )
True
False
2 7
= 3 4
2 7 8
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8 )
True
False
2 7
= 3 4
2 7 8
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FALSE
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9 )
3940
8 10
= 4 5
4042
A 1
B
C
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9 )
3940
8 10
= 4 5
4042
A 1
B
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A
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10 )
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10 )
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11 )
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Sometimes you can cross simplify prior to multiplying.
without cross simplifying
with cross simplifying
3
1
2
5
Simplify
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12 Can this problem be cross simplified?
Yes
No
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12 Can this problem be cross simplified?
Yes
No
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YES
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13 Can this problem be cross simplified?
Yes
No
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13 Can this problem be cross simplified?
Yes
No
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NO
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14 Can this problem be cross simplified?
Yes
No
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14 Can this problem be cross simplified?
Yes
No
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NO
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15 Can this problem be cross simplified?
Yes
No
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15 Can this problem be cross simplified?
Yes
No
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YES
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16 )
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16 )
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A mixed number can be divided by a mixed number using the following visual model.
First find the least common denominator (LCD) which is 6.
If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?
Visual Model
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A mixed number can be divided by a mixed number using the following visual model.
First find the least common denominator (LCD) which is 6.
If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit?
Visual Model
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Ans
wer
18
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Since our LCD is 6, every 6 lines is considered a whole.
1 1/2 is equivalent to 9 sections on the number line.
1 1/2
2 2/3 is equivalent to 16 sections on the number line.
So 1 1/2 ÷ 2 2/3 = 9/16
2 2/3
Visual Model
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1/2
2 2/3
1 1/2
What if the problem were written as ?
How many times does 1 1/2 divide into 2 2/3?
Visual Model
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Step 1: Rewrite the Mixed Number(s) as an improper fraction(s). (write whole numbers / 1)
Step 2: Follow the same steps for dividing fractions
Dividing Mixed Numbers Algorithm
6 1
x 2 3
= 12 3
=6 1 2
1 6 1
3 2
= = 4
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5 3
x 2 7
= 1021
2 3
=1 1 2
3 5 3
7 2
=
Example
Evaluate:
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20 )
= 1 2
2 2 3
1
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20 )
= 1 2
2 2 3
1
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21 )
= 1 2
52
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21 )
= 1 2
52
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22 )
= 2 5
5 1 2
4
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22 )
= 2 5
5 1 2
4
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23 )
= 1 2
2 3 8
3
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23 )
= 1 2
2 3 8
3
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Winnie needs pieces of string for a craft project. How many 1/6 yd pieces of string can she cut from a piece that is 2/3 yd long?
16
23 ÷
23
x 61
123 == 4 pieces4
1
or
23
x 61 =
1
241
= 4 pieces
Application Problem
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One student brings 1/2 yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbons will each student receive?
12 ÷ 3
12
x 13
16
yards of ribbon=
Application Problem
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Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs can she cut?
6 ÷34
61
÷ 34
61 x 4
3 = 243
81 8 rungs= =
Application Problem
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A box weighing 9 1/3 lb contains toy robots weighing 1 1/6 lb apiece. How many toy robots are in the box?
9 13
1 16÷
283
76÷
67
283
x
1
4
1
2
= 81
8 robots=
Application Problem
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24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion?
A 8 pounds
B 4 1/2 pounds
C 2/5 pounds
D 1/8 pound
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24 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion?
A 8 pounds
B 4 1/2 pounds
C 2/5 pounds
D 1/8 pound
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D
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25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel?
A 84 miles
B 62 miles
C 42 miles
D 38 miles
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25 A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel?
A 84 miles
B 62 miles
C 42 miles
D 38 miles
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D
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26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use?
A 48 tablespoons
B 24 tablespoons
C 12 tablespoons
D 6 tablespoons
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26 One tablespoon is equal to 1/16 cup. It is also equal to 1/2 ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use?
A 48 tablespoons
B 24 tablespoons
C 12 tablespoons
D 6 tablespoons
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C
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27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book?
A 5/12 pound
B 2 2/5 pounds
C 8 2/5 pounds
D 86 2/5 pounds
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27 A bookstore packs 6 books in a box. The total weight of the books is 14 2/5 pounds. If each book has the same weight, what is the weight of one book?
A 5/12 pound
B 2 2/5 pounds
C 8 2/5 pounds
D 86 2/5 pounds
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B
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28 There is gallon of distilled water in the
class science supplies. If each pair of
students doing an experiment uses
gallon of distilled water, there will be
gallon left in the supplies . How many
students are doing the experiments?
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28 There is gallon of distilled water in the
class science supplies. If each pair of
students doing an experiment uses
gallon of distilled water, there will be
gallon left in the supplies . How many
students are doing the experiments?
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29 Carol makes cups of snack mix. She
puts all the snack mix into plastic bags. She
puts cup of the snack mix in each bag.
How many plastic bags does Carol need?
Enter your answer in the box.
bags
From PARCC EOY sample test non-calculator #9
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29 Carol makes cups of snack mix. She
puts all the snack mix into plastic bags. She
puts cup of the snack mix in each bag.
How many plastic bags does Carol need?
Enter your answer in the box.
bags
From PARCC EOY sample test non-calculator #9
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& M
ath
Prac
tice
14 bags
MP 4
Word problems allow students to recognize math in everyday like and use the math they know to solve problems.
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30 Part AA group of hikers buy 8 bags of trail mix.
Each bag contains cups of trail mix. The
trail mix is shared evenly among 12 hikers.
How many cups of trail mix will each hiker
receive? Show your work or explain your
answer.
From PARCC PBA sample test calculator #10
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30 Part AA group of hikers buy 8 bags of trail mix.
Each bag contains cups of trail mix. The
trail mix is shared evenly among 12 hikers.
How many cups of trail mix will each hiker
receive? Show your work or explain your
answer.
From PARCC PBA sample test calculator #10
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31 Part BThe hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout.· Determine the total distance each hiker
will hike. Show your work or explain your answer.
From PARCC PBA sample test calculator #10
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31 Part BThe hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout.· Determine the total distance each hiker
will hike. Show your work or explain your answer.
From PARCC PBA sample test calculator #10
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32 Part B (continued)· Determine the total number of gallons of
water each hiker will bring. Show your work or explain your answer.
From PARCC PBA sample test calculator #10
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32 Part B (continued)· Determine the total number of gallons of
water each hiker will bring. Show your work or explain your answer.
From PARCC PBA sample test calculator #10
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33 This diagram shows a number line.
Part A
James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board.
From PARCC PBA sample test calculator #8
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33 This diagram shows a number line.
Part A
James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board.
From PARCC PBA sample test calculator #8
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The number line diagram show segments marked that are spaces 1/8 unit apart. I know James' board is 3/4 foot long. I counted the number of 1/8 units until I got to 3/4 on the number line. There are 6 of these. So James can cut a total of 6 pieces from the board.
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34 Part B
Write an equation using division that represents how James can find the number of pieces he can cut from the board.
From PARCC PBA sample test calculator #8
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34 Part B
Write an equation using division that represents how James can find the number of pieces he can cut from the board.
From PARCC PBA sample test calculator #8
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Long Division Review
Return toTable ofContents
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Some division terms to remember....· The number to be divided into is known as the dividend
· The number which divides the other number is known as the divisor
· The answer to a division problem is called the quotient
divisor 5 20 dividend
4 quotient
20 ÷ 5 = 420__5
= 4
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When we are dividing, we are breaking apart into equal groups
EXAMPLE 1
Find 132 3
Step 1: Can 3 go into 1, no so can 3 go into 13, yes
4
- 12 1
3 x 4 = 1213 - 12 = 1Compare 1 < 3
3 132
3 x 4 = 1212 - 12 = 0Compare 0 < 3
- 12 0
Step 2: Bring down the 2. Can 3 go into 12, yes
2
4
Click for step 1
Click for step 2
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Step 3: Check your answer.
44 x 3 132
click
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Estimating Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
What place value should we round to?
Round to the largest place value.
357 rounds to ____
15 rounds to ____
Our answer should approximately be ...
20
357 ÷ 15
click
click
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EXAMPLE 2(change pages to see each step)
Step 1: Can 15 go into 3, no so can 15 go into 35, yes
2
-30 5
15 x 2 = 3035 - 30 = 5Compare 5 < 15
15 357
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2
-30 5
15 35715 x 3 = 4557 - 45 =12Compare 12 < 15
7 - 45 12
Step 2 : Bring down the 7. Can 25 go into 207, yes
3
EXAMPLE 2(change pages to see each step)
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2
-30 5
15 357.0
7 - 45 120 - 120 0
3
Step 3: You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division.
15 x 8 = 120120 - 120 = 0Compare 0 < 15
.8
EXAMPLE 2(change pages to see each step)
Is our answer close to our estimate?
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Check your answer.
23.8 x 15
357click
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Estimate the following problems. Discuss your answers with your group.
35 300
15 20
click
clickclick
click
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Now solve the following problems. Discuss your answers with your group.
41 324
19.5 23.2
click
click click
click
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35 Estimate the quotient.
779 ÷ 19
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35 Estimate the quotient.
779 ÷ 19
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40
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36 Compute.
779 ÷ 19 =
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36 Compute.
779 ÷ 19 =
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41
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37 Estimate the quotient.
1,551 ÷ 55
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37 Estimate the quotient.
1,551 ÷ 55
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Approximately 33
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38 Compute.
1,551 ÷ 55 =
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38 Compute.
1,551 ÷ 55 =
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28.2
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39 Estimate the quotient.
1,288 ÷ 35
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39 Estimate the quotient.
1,288 ÷ 35
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25
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40 Compute.
1,288 ÷ 35 =
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40 Compute.
1,288 ÷ 35 =
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36.8
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41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.
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41 The school concert hall contains 312 chairs in 12 rows. Estimate how many chairs are in each row.
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30
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42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?
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42 The school concert hall contains 312 chairs in 12 rows. How many chairs are in each row?
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26
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43 Compute.
4706 ÷ 104 =
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43 Compute.
4706 ÷ 104 =
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45.25
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44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?
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44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day?
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49
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45 Compute.
1032 ÷ 24 =
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45 Compute.
1032 ÷ 24 =
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43
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46 Compute.
4922 ÷ 92 =
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46 Compute.
4922 ÷ 92 =
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53.5
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47 Enter your answer in the box.
34,992 ÷ 81 =
From PARCC EOY sample test non-calculator #18
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47 Enter your answer in the box.
34,992 ÷ 81 =
From PARCC EOY sample test non-calculator #18
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Ans
wer
432
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Adding Decimals
Return toTable ofContents
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If you know how to add whole numbers then you can add decimals. Just follow these few steps.
Step 1: Put the numbers in a vertical column, aligning the decimal points.
Step 2: Add each column of digits, starting on the right and working to the left.
Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.
Adding Decimals
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When adding or subtracting decimals, always remember to align the decimals vertically...
0.250.250.250.251.00+
Adding Decimals
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When adding or subtracting decimals, always remember to align the decimals vertically...
0.250.250.250.251.00+
Adding Decimals
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Mat
h Pr
actic
e
MP 5
Students who struggle to line up the digits correctly for an addition of decimals problem may find it useful to line them up using graph paper. This will help them to choose to use graph paper as a tool to help them solve problems.
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Estimating Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
What place value should we round to?
Round to the nearest whole number.
5.1 rounds to ____
1.25 rounds to ____
0.04 rounds to ____
1.99 rounds to ____
Our answer should approximately be ...
8
5.1 + 1.25 + 0.04 + 1.99
click
click
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Now, try this - Don't forget - LINE THEM UP
5.1 + 1.25 + 0.04 + 1.99
5.101.250.041.99+
8.38
You can add a zero as a place holder to help line your numbers up.
Adding Decimals
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TRY THESE.Estimate the following sums in your notebook. Check with the rest of your group.
1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9
3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656
8 + 4 + 0 = 12 3 + 12 + 9 = 24
17 + 3 + 8 = 28 10 + 3 + 5 = 18
click
click
click
click
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TRY THESE.Complete in your notebook then check with the rest of your group.
1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9
8.23 3.178 4.125 12.28 + 0.1189 + 9. 12.4739 24.458
3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656
17.009 9.999 2.965 3.1567 + 8.4 + 4.5656 28.374 17.7213
click click
click click
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TRY THESE.Complete in your notebook then check with the rest of your group.
1) 8.23 + 4.125 + 0.1189 2) 3.178 + 12.28 + 9
8.23 3.178 4.125 12.28 + 0.1189 + 9. 12.4739 24.458
3) 17.009 + 2.965 + 8.4 4) 9.999 + 3.1567 + 4.5656
17.009 9.999 2.965 3.1567 + 8.4 + 4.5656 28.374 17.7213
click click
click click
[This object is a pull tab]
Mat
h Pr
actic
e MP 1
Remind students to compare their estimates to their exact answers to see if their exact answers make sense.
Slide 95 (Answer) / 215
48 Add the following:
0.6 + 0.55 =
A 6.1
B 0.115
C 1.15
D 0.16
Slide 96 / 215
48 Add the following:
0.6 + 0.55 =
A 6.1
B 0.115
C 1.15
D 0.16[This object is a pull tab]
Ans
wer
C
Slide 96 (Answer) / 215
49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why?
A JoanneB Peter
Slide 97 / 215
49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately 2. Peter disagrees and says the sum should be approximately 0. Who is correct? Why?
A JoanneB Peter
[This object is a pull tab]
Ans
wer
Joanne is correct because 0.6 rounds to 1 and 0.55 rounds to 1. So the estimation is 2. Peter only looked at the whole number and did not round the decimals.
Slide 97 (Answer) / 215
50 Find the sum.
1.025 + 0.03 + 14.0001 =
Slide 98 / 215
50 Find the sum.
1.025 + 0.03 + 14.0001 =
[This object is a pull tab]
Ans
wer
15.0551
Slide 98 (Answer) / 215
51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games.
Slide 99 / 215
51 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. Estimate how much Franco spent on the video games.
[This object is a pull tab]
Ans
wer
$66
Slide 99 (Answer) / 215
52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games?
Slide 100 / 215
52 Franco went to buy new video games. He bought MaxRush for $19.95, Duplo Race for $23.95 and Garage Mate for $21.95. How much did he spend on video games?
[This object is a pull tab]
Ans
wer
$65.85
Slide 100 (Answer) / 215
53 What is the sum of
12.034 and 0.0104?
A 12.1344
B 12.0444
C 12.138
D 1.20444
Slide 101 / 215
53 What is the sum of
12.034 and 0.0104?
A 12.1344
B 12.0444
C 12.138
D 1.20444 [This object is a pull tab]
Ans
wer
B
Slide 101 (Answer) / 215
54 Estimate the sum.
8.5 + 0.042 + 12.31
A 20B 21C 22D 23
Slide 102 / 215
54 Estimate the sum.
8.5 + 0.042 + 12.31
A 20B 21C 22D 23
[This object is a pull tab]
Ans
wer
B
Slide 102 (Answer) / 215
55 Find the sum.
8.5 + 0.042 + 12.31 =
A 13.58
B 21.23
C 20.852
D 20.14
Slide 103 / 215
55 Find the sum.
8.5 + 0.042 + 12.31 =
A 13.58
B 21.23
C 20.852
D 20.14
[This object is a pull tab]
Ans
wer
C
Slide 103 (Answer) / 215
56 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled?
A .561 cm.B .452 cm.
C .480 cm.
D .473 cm.
Slide 104 / 215
56 Five students collected paper to be recycled. Shelly's stack was .008 cm. thick; Ken's stack was .125 cm. thick; Joe's stack was .150 cm. thick; Betty's stack was .185 cm. thick; Mary's stack was .005 cm. thick. What was the thickness of the papers collected to be recycled?
A .561 cm.B .452 cm.
C .480 cm.
D .473 cm.
[This object is a pull tab]
Ans
wer
D
Slide 104 (Answer) / 215
57 Find the sum.
5 + 100.145 + 57.8962 + 2.312 =
Slide 105 / 215
57 Find the sum.
5 + 100.145 + 57.8962 + 2.312 =
[This object is a pull tab]
Ans
wer
165.3532
Slide 105 (Answer) / 215
58 What is the sum of 74.835 and 2.67?
Enter your answer in the box.
From PARCC EOY sample test non-calculator #19
Slide 106 / 215
58 What is the sum of 74.835 and 2.67?
Enter your answer in the box.
From PARCC EOY sample test non-calculator #19
[This object is a pull tab]
Ans
wer
77.505
Slide 106 (Answer) / 215
Let's go to Cool Math and practice addition.
Cool Math Link
Web Link
Slide 107 / 215
Subtracting Decimals
Return toTable ofContents
Slide 108 / 215
If you know how to subtract whole numbers then you can subtract decimals. Just follow these few steps.
Step 1: Put the numbers in a vertical column, aligning the decimal points.
Step 2: Subtract the numbers from right to left using the same rules as whole numbers.
Step 3: Place the decimal point in the answer directly below the decimal points that you lined up in Step 1.
1.1- 0.3
1.1- 0.3
0.8
0 1
Subtracting Decimals
Slide 109 / 215
Estimating Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
21.7 - 8.21
What place value should we round to?
Round to the nearest whole number.
21.7 rounds to ____
8.21 rounds to ____
Our answer should approximately be ...
14click
click
Slide 110 / 215
What do we do if there aren't enough decimal places when we subtract?
21.7 - 8.21
Don't forget...Line Them Up!
21.7 8.21
What goes here?
21.70 8.2113.49
6111
Subtracting Decimals
Slide 111 / 215
TRY THESE.Estimate the following differences in your notebook. Then check with the rest of your group.
1) 8.23 - 0.1189 2) 12.283 - 9.025
3) 17.009 - 8.4 4) 9.999 - 4.5656
8 - 0 = 8 12 - 9 = 3
10 - 5 = 517 - 8 = 9
click click
click click
Slide 112 / 215
TRY THESE.Complete in your notebook then check with the rest of your group.
1) 8.23 - 0.1189 2) 12.283 - 9.025
8.23 12.283 - 0.1189 - 9.025 8.1111 3.258
3) 17.009 - 8.4 4) 9.999 - 4.5656
17.009 9.999 - 8.4 - 4.5656 8.609 5.4334
click
click
click
click
Slide 113 / 215
TRY THESE.Complete in your notebook then check with the rest of your group.
1) 8.23 - 0.1189 2) 12.283 - 9.025
8.23 12.283 - 0.1189 - 9.025 8.1111 3.258
3) 17.009 - 8.4 4) 9.999 - 4.5656
17.009 9.999 - 8.4 - 4.5656 8.609 5.4334
click
click
click
click[This object is a pull tab]
Mat
h Pr
actic
e MP 1
Remind students to compare their estimates to their exact answers to see if their exact answers make sense.
Slide 113 (Answer) / 215
59 ) 5 - 0.238 =
Slide 114 / 215
59 ) 5 - 0.238 =
[This object is a pull tab]
Ans
wer
4.762
Slide 114 (Answer) / 215
60 ) 12.809 - 4 =
Slide 115 / 215
60 ) 12.809 - 4 =
[This object is a pull tab]
Ans
wer
8.809
Slide 115 (Answer) / 215
61 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit?
A $20B $18C $13D $12
Slide 116 / 215
61 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. What is the estimate of Sally's profit?
A $20B $18C $13D $12
[This object is a pull tab]
Ans
wer
D
Slide 116 (Answer) / 215
62 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit ?
A $37.57
B $12.43
C $13.57
D $12.00
Slide 117 / 215
62 Sally won $25.00 for her science fair project. Her project cost $12.57 to prepare. How much did Sally actually make as a profit ?
A $37.57
B $12.43
C $13.57
D $12.00
[This object is a pull tab]
Ans
wer
B
Slide 117 (Answer) / 215
63 ) 1897.112 - 0.647 =
Slide 118 / 215
63 ) 1897.112 - 0.647 =
[This object is a pull tab]
Ans
wer
1896.465
Slide 118 (Answer) / 215
64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max?
Slide 119 / 215
64 The Johnson twins raced each other in the 200-meter dash. Jordan finished in 23.48 seconds, and Max finished in 26.13 seconds. How much faster was Jordan than Max?
[This object is a pull tab]
Ans
wer
2.65 seconds
Slide 119 (Answer) / 215
65 Timothy is working on the problem 4.1 - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not?YesNo
Slide 120 / 215
65 Timothy is working on the problem 4.1 - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4.1 and 0.1 to estimate the answer. Is he correct in doing so? Why or why not?YesNo
[This object is a pull tab]
Ans
wer
Timothy is correct but he still has to use decimals instead of whole numbers. He would get the same
estimate for this problem if he rounded to the nearest whole
number.
Slide 120 (Answer) / 215
66 ) 4.1 - 0.094 =
Slide 121 / 215
66 ) 4.1 - 0.094 =
[This object is a pull tab]
Ans
wer
4.006
Slide 121 (Answer) / 215
67 ) 17 - 13.008 =
Slide 122 / 215
67 ) 17 - 13.008 =
[This object is a pull tab]
Ans
wer
3.992
Slide 122 (Answer) / 215
68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths?
A 27.85 - 12.91B 14.17 - 8.2C 7.9 - 3.88D 21.25 - 18.16
Slide 123 / 215
68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths?
A 27.85 - 12.91B 14.17 - 8.2C 7.9 - 3.88D 21.25 - 18.16
[This object is a pull tab]
Ans
wer
D
Slide 123 (Answer) / 215
69 If you buy two movie tickets for $8.25 each, what will your change be from $20?
Slide 124 / 215
69 If you buy two movie tickets for $8.25 each, what will your change be from $20?
[This object is a pull tab]
Ans
wer
$3.50
Slide 124 (Answer) / 215
Cool Math Link
Let's go to Cool Math and practice subtraction.
Web Link
Slide 125 / 215
The Distributive Property and
the Product of Decimals
Return toTable ofContents
Slide 126 / 215
If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps.
Step 1: Ignore the decimal points.
Step 2: Multiply the numbers using the same rules as whole numbers.
Step 3: Count the total number of digits to the right of the decimal point. Put that many digits to the right of the decimal point in your answer.
Multiplication
Slide 127 / 215
Evaluate 200 x 41.5
8,300
We can also use the distributive property to calculate the product.
200 x 41.5
200 x (41 + 0.5)
(200 x 41) + (200 x 0.5)
8,200 + 100 = 8,300
Separate 41.5 into an addition expression with two addends
Apply the distributive property
Apply the order of operations
click
Distributive Property
Slide 128 / 215
Evaluate 200 x 41.5
8,300
We can also use the distributive property to calculate the product.
200 x 41.5
200 x (41 + 0.5)
(200 x 41) + (200 x 0.5)
8,200 + 100 = 8,300
Separate 41.5 into an addition expression with two addends
Apply the distributive property
Apply the order of operations
click
Distributive Property
[This object is a pull tab]
Mat
h Pr
actic
e MP 7
The use of the distributive property will help students to see the structure of the problem.
Slide 128 (Answer) / 215
Evaluate 400 x 18.33
400 x ( ________ + ________ )
(400 x ________ ) + (400 x ________ )
________ + ________ = ________7332
This method is known as partial products.
Distributive Property
Slide 129 / 215
How can we use partial products to calculate the area of the rectangle shown below?
58 ft
200 ft
0.6 ft200 x 58.6
200 x ( ________ + ________ )
(200 x ________ ) + (200 x ________ )
________ + ________ = ________11,720
Click to reveal
58.6 ft
200 ft
Distributive Property
Slide 130 / 215
How can we use partial products to calculate the area of the rectangle shown below?
58 ft
200 ft
0.6 ft200 x 58.6
200 x ( ________ + ________ )
(200 x ________ ) + (200 x ________ )
________ + ________ = ________11,720
Click to reveal
58.6 ft
200 ft
Distributive Property
[This object is a pull tab]
Teac
her N
otes
Click on the yellow box to show the visual
representation of partial products.
Slide 130 (Answer) / 215
70 ) 12(43) = 12(40) x 12(3)
TrueFalse
Slide 131 / 215
70 ) 12(43) = 12(40) x 12(3)
TrueFalse
[This object is a pull tab]
Ans
wer
FALSE
Slide 131 (Answer) / 215
71 Use the distributive property to rewrite the expression.
3(76.8) Students type their answers here
Slide 132 / 215
71 Use the distributive property to rewrite the expression.
3(76.8) Students type their answers here
[This object is a pull tab]
Ans
wer
3(76 + 0.8)
Slide 132 (Answer) / 215
72 Calculate the product using partial products.
5(48)
Slide 133 / 215
72 Calculate the product using partial products.
5(48)
[This object is a pull tab]
Ans
wer
240
Slide 133 (Answer) / 215
73 Calculate the product using partial products.
13(5.2)
Slide 134 / 215
73 Calculate the product using partial products.
13(5.2)
[This object is a pull tab]
Ans
wer
67.6
Slide 134 (Answer) / 215
74 Calculate the product using partial products.
300(7.4)
Slide 135 / 215
74 Calculate the product using partial products.
300(7.4)
[This object is a pull tab]
Ans
wer
2,220
Slide 135 (Answer) / 215
75 Calculate the product using partial products.
200(6.5)
Slide 136 / 215
75 Calculate the product using partial products.
200(6.5)
[This object is a pull tab]
Ans
wer
1,300
Slide 136 (Answer) / 215
76 Calculate the area of the rectangle using partial products.
300units
43.9 units
Slide 137 / 215
76 Calculate the area of the rectangle using partial products.
300units
43.9 units
[This object is a pull tab]
Ans
wer
13,170
Slide 137 (Answer) / 215
Multiplying Decimals
Return toTable ofContents
Slide 138 / 215
Convert the following decimal numbers into fractions.
0.7 x 0.09
What is the product?
631000
We multiplied seven tenths by nine hundredths.What place value will the last digit in the product be in if we convert it into a decimal number?
Thousandths
click
click
Multiplication
Slide 139 / 215
Try These!What place value will the last digit be in for the following problems? Don't forget to convert them to fractions first.
Fractions Product Place Value
1) 0.3 x 0.7
2) 0.2 x 0.13
3) 0.08 x 0.231
Slide 140 / 215
Do you notice a pattern for multiplying decimals?
3.5 x 1.72
3 510 1 72
100x
3510
x 172100
60201000
Where does the decimal point go? Drag the decimal point.
6 0 2 0
Multiplication
Slide 141 / 215
If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps.
Step 1: Ignore the decimal points.
Step 2: Multiply the numbers using the same rules as whole numbers.
Step 3: Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer.
Multiplication
Slide 142 / 215
3.21x .04
.1284
There are a total of four digits to the right of the decimal points.
There must be four digits to the right of the decimal point in the answer.
} 2 digits
Multiplication
} 2 digits
Slide 143 / 215
Estimate Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
23.2 x 4.04
What place value should we round to?
Round to the nearest whole number.
23.2 rounds to ____
4.04 rounds to ____
Our answer should approximately be ...
92click
click
Slide 144 / 215
23.2x 4.04
928
92800 0000
93.728
} 1 digit
There are a total of three digits to the right of the decimal points.
There must be three digits to the right of the decimal point in the answer.
Estimating helps us recognize where the decimal point belongs!
Exact Answer
} 2 digits
Slide 145 / 215
Estimate your answer for the following problem by rounding the numbers to the nearest whole number.
9.5 x 0.05
9.5 rounds to _____
0.05 rounds to _____
What is your estimate?
For problems like these, use your number sense!
You are multiplying 9.5 by 0.05 which means you are taking a part (fraction) of 9.5.
So your answer must be smaller than 9.5!click
Estimate Your Answer
Slide 146 / 215
smallerthan 3.214
TRY THESE.Estimate the following products in your notebook then check with the rest of your group.
1) 14.512 2) 8.31 x 4.21 x 1.008
3) 7.0045 4) 3.214 x 5.2 x 0.0034
15 x 4 = 60 8 x 1 = 8
7 x 5 = 35
click
clickclick
click
Slide 147 / 215
TRY THESE.Complete in your notebook then check with the rest of your group.
1) 14.512 2) 8.31 x 4.21 x 1.008 14512 290240 5804800 61.09552
3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340
66480000
00000831000
8.37648
1285696420
0.0109276
click
click
click
click
Slide 148 / 215
TRY THESE.Complete in your notebook then check with the rest of your group.
1) 14.512 2) 8.31 x 4.21 x 1.008 14512 290240 5804800 61.09552
3) 7.0045 4) 3.214 x 5.2 x 0.0034 140090 3502250 36.42340
66480000
00000831000
8.37648
1285696420
0.0109276
click
click
click
click
[This object is a pull tab]
Mat
h Pr
actic
e MP 1
Remind students to compare their estimates to their exact answers to see if their exact answers make sense.
Slide 148 (Answer) / 215
77 Estimate the product.
0.42 x 0.032
A The product will be less than 1B The product will be equal to 1C The product will be greater than 1
Slide 149 / 215
77 Estimate the product.
0.42 x 0.032
A The product will be less than 1B The product will be equal to 1C The product will be greater than 1
[This object is a pull tab]
Ans
wer
A
Slide 149 (Answer) / 215
78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point.
TrueFalse
Slide 150 / 215
78 The product of 0.42 x 0.032 will have 4 digits to the right of the decimal point.
TrueFalse
[This object is a pull tab]
Ans
wer
False
Slide 150 (Answer) / 215
79 Multiply 0.42 x 0.032
Slide 151 / 215
79 Multiply 0.42 x 0.032
[This object is a pull tab]
Ans
wer
0.1344
Slide 151 (Answer) / 215
80 Multiply 3.452 x 2.1
Slide 152 / 215
80 Multiply 3.452 x 2.1
[This object is a pull tab]
Ans
wer
7.2492
Slide 152 (Answer) / 215
81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money?
Estimate to determine your answer. Do not solve.
YesNo
Slide 153 / 215
81 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money?
Estimate to determine your answer. Do not solve.
YesNo
[This object is a pull tab]
Ans
wer
NO
Slide 153 (Answer) / 215
82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost?
Slide 154 / 215
82 You need to buy 6 notebooks that cost $0.87 each. How much will this cost?
[This object is a pull tab]
Ans
wer
$5.22
Slide 154 (Answer) / 215
83 Multiply 53.24 x 0.089
Slide 155 / 215
83 Multiply 53.24 x 0.089
[This object is a pull tab]
Ans
wer
4.73836
Slide 155 (Answer) / 215
84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50.
What would the total cost be of four pairs
of jeans on sale?
A $119.96B $90.00
C $86.00
D $52.49
Slide 156 / 215
84 The regular price of a pair of jeans is $29.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $22.50.
What would the total cost be of four pairs
of jeans on sale?
A $119.96B $90.00
C $86.00
D $52.49
[This object is a pull tab]
Ans
wer
B
Slide 156 (Answer) / 215
85 How many digits will be to the right of decimal point in the product for the problem 4.0156 x 7.8?
A 2B 3C 4D 5
Slide 157 / 215
85 How many digits will be to the right of decimal point in the product for the problem 4.0156 x 7.8?
A 2B 3C 4D 5
[This object is a pull tab]
Ans
wer
D
Slide 157 (Answer) / 215
86 Multiply 4.0156 x 7.8
Slide 158 / 215
86 Multiply 4.0156 x 7.8
[This object is a pull tab]
Ans
wer
31.32168
Slide 158 (Answer) / 215
87 Multiply 0.012 x 0.21
Slide 159 / 215
87 Multiply 0.012 x 0.21
[This object is a pull tab]
Ans
wer
0.00252
Slide 159 (Answer) / 215
88 Enter your answer in the box.
18.3 x 4.39 =
From PARCC EOY sample test non-calculator #7
Slide 160 / 215
88 Enter your answer in the box.
18.3 x 4.39 =
From PARCC EOY sample test non-calculator #7
[This object is a pull tab]
Ans
wer
80.337
Slide 160 (Answer) / 215
89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event.
How much profit, in dollars, will Thomas earn if he sells all the bottles of water?
Enter your answer in the box.
$
From PARCC EOY sample test non-calculator #17
Slide 161 / 215
89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event.
How much profit, in dollars, will Thomas earn if he sells all the bottles of water?
Enter your answer in the box.
$
From PARCC EOY sample test non-calculator #17
[This object is a pull tab]
Ans
wer
& M
ath
Prac
tice
$22.31
MP 2
Make sure to also check that the students have used good reasoning habits and can show an understandable representation of the problem solved.
Slide 161 (Answer) / 215
Dividing Decimals
Return toTable ofContents
Slide 162 / 215
Divide Decimals by Whole Numbers
56.08
28 04
2
Step 1: Use long division.
Step 2: Bring the decimal point up into the quotient.
Slide 163 / 215
Try This!
12.45 ÷ 5 =
Slide 164 / 215
Try This!
12.45 ÷ 5 =
[This object is a pull tab]
Ans
wer
2.49
Slide 164 (Answer) / 215
The Power of Ten10
Multiplying by a power of ten makes dividing by decimals easier!
1) 13 x 10 = _______
2) 94 x 100 = _______
3) 28 x 1000 = _______
4) 6.2 x 10 = _______
5) 4.78 x 100 = _______
6) 51.293 x 1000 = _______
Do you see a pattern for multiplying by a power of ten?
The decimal point moves to the right depending on the number of zeros in the power of ten!Click to
Reveal
Slide 165 / 215
The Power of Ten10
Multiplying by a power of ten makes dividing by decimals easier!
1) 13 x 10 = _______
2) 94 x 100 = _______
3) 28 x 1000 = _______
4) 6.2 x 10 = _______
5) 4.78 x 100 = _______
6) 51.293 x 1000 = _______
Do you see a pattern for multiplying by a power of ten?
The decimal point moves to the right depending on the number of zeros in the power of ten!Click to
Reveal
[This object is a pull tab]
Mat
h Pr
actic
e MP 8
Noticing the pattern when multiplying by a power of ten will help students to understand the algorithm for multiplication of decimals.
Slide 165 (Answer) / 215
Divisor Dividend
Step 1: Change the divisor to a whole number by multiplying by a power of 10.
Step 2: Multiply the dividend by the same power of 10.
Step 3: Use long division.
Step 4: Bring the decimal point up into the quotient.
Divide by Decimals
Quotient
Slide 166 / 215
15.6 6.24
Multiply by 10, so that 15.6 becomes 1566.24 must also be multiplied by 10
156 62.4
.234 23.4
Multiply by 1000, so that .234 becomes 23423.4 must also be multiplied by 1000
234 23400
Try rewriting these problems so you are ready to divide!
Power of Ten
Slide 167 / 215
6789.2109
415 25020
Rewrite each problem after multiplying by a power of 10.
1)
2)
3)
4)
250.2 ÷ 4.15
.008
0.9
68.342 ÷ 2.2
4.2
678.921
4200008
22 683.42
Power of Ten
click
click
click
click
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Estimating Your AnswerBefore any calculations, estimate your answer to make sure you are on the right track.
23.2 ÷ 4.04
What place value should we round to?
Round to the nearest whole number.
23.2 rounds to ____
4.04 rounds to ____
Our answer should approximately be ...
5click
click
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4.04 23.2
Try This! Be sure to round your answer to the thousandths.
5.743click
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Estimate your answer for the following problem by rounding the numbers to the nearest whole number.
9.5 ÷ 0.05
9.5 rounds to _____
0.05 rounds to _____
What is your estimate?
For problems like these, use your number sense!
If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5?
Your answer must be greater than 9.5!click
Estimate
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Estimate your answer for the following problem by rounding the numbers to the nearest whole number.
9.5 ÷ 0.05
9.5 rounds to _____
0.05 rounds to _____
What is your estimate?
For problems like these, use your number sense!
If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5?
Your answer must be greater than 9.5!click
Estimate
[This object is a pull tab]
Mat
h Pr
actic
e MP 6
This standard is addressed when you ask the students if they will get a quotient smaller or greater than 9.5
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90 Divide
0.78 ÷ 0.02 =
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90 Divide
0.78 ÷ 0.02 =
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Ans
wer
39
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91 Use estimation to figure out if the quotient will be
A less than 4.866
B around 4.866
C greater than 4.866
4.866 ÷ 0.6
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91 Use estimation to figure out if the quotient will be
A less than 4.866
B around 4.866
C greater than 4.866
4.866 ÷ 0.6
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Ans
wer
C
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92
0.6 4.866
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92
0.6 4.866
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Ans
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8.11
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93 ) 10 divided by 0.25 =
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93 ) 10 divided by 0.25 =
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Ans
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40
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94 ) 12.03 ÷ 0.04 =
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94 ) 12.03 ÷ 0.04 =
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Ans
wer
300.75
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95
0.012 24.6
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95
0.012 24.6
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Ans
wer
2050
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96 Estimate.
36 ÷ 1.2
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96 Estimate.
36 ÷ 1.2
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Ans
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36
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97 Evaluate.
36 ÷ 1.2 =
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97 Evaluate.
36 ÷ 1.2 =
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Ans
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30
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98 Estimate.
9.116 ÷ 2.12
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98 Estimate.
9.116 ÷ 2.12
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Ans
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4.5
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99 Evaluate.
9.116 ÷ 2.12 =
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99 Evaluate.
9.116 ÷ 2.12 =
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Ans
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4.3
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100 Enter your answer in the box.
33.8 ÷ 32.5 =
From PARCC EOY sample test #2 non-calculator
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100 Enter your answer in the box.
33.8 ÷ 32.5 =
From PARCC EOY sample test #2 non-calculator
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Ans
wer
1.04
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There are two types of decimals - terminating and repeating.
A terminating decimal is a decimal that ends.All of the examples we have completed so far are terminating.
A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern.
To denote a repeating decimal, a line is drawn above the numbers that repeat. However, with a calculator, the last digit is rounded.
Terminating and Repeating
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Let's consider the following...
Click to Reveal
Terminating or Repeating
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Let's consider the following...
Click to Reveal
Terminating or Repeating
[This object is a pull tab]
Teac
her N
otes
Explain how this is a repeating decimal and how
we put a bar over the numbers that repeat.
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63 48 45 39 36 32 27 51 45 60 54 6
Click to Reveal
Repeating Example
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6600 2342 2200 14200 13200 10000 8800 12000 11000 10000 8800 12000 11000
Click to Reveal
Repeating Example
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101 ) 15.5 ÷ 0.3
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101 ) 15.5 ÷ 0.3
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Ans
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102 ) 0.8 ÷ 0.003 =
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102 ) 0.8 ÷ 0.003 =
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Ans
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103 You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy?
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103 You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $20 bill on you. How many gallons can you buy?
[This object is a pull tab]
Ans
wer 5.571
gallons
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104 ) 25 ÷ 1.1 =
A 2.27B 22.73C 22.7D 22.72
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104 ) 25 ÷ 1.1 =
A 2.27B 22.73C 22.7D 22.72
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Ans
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D
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105
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105
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Ans
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106 If 6 people are on an elevator and together they weigh 931.56 pounds, find the average weight of each person.
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106 If 6 people are on an elevator and together they weigh 931.56 pounds, find the average weight of each person.
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Ans
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155.26 pounds
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107 ) 0.007 ÷ 0.9 =
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107 ) 0.007 ÷ 0.9 =
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Ans
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108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?
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108 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag?
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Ans
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0.647 lbs
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109
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109
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110 ) 91.84 ÷ 4.8 =
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110 ) 91.84 ÷ 4.8 =
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Ans
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111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days?
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111 Texas suffered through a heat wave in August 2011. The highest four temperatures (in degrees Fahrenheit) were 103.4, 102.8, 101.9 and 102.5. What was the average temperature for those four days?
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Ans
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102.65o F
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112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?
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112 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.10 on one pattern and $8.40 on another. How much does one yard cost?
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Ans
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$5.00
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113 ) 9 ÷ 0.22
A 40.9B 40.90C 40.91D 40.9
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113 ) 9 ÷ 0.22
A 40.9B 40.90C 40.91D 40.9
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Ans
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B
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Glossary & Standards
Return to Table of Contents
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Glossary & Standards
Return to Table of Contents
[This object is a pull tab]
Teac
her N
otes Vocabulary Words are bolded
in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
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Algorithm
A step-by-step process to find a solution.
It's like a cooking
recipe for mathematics.
24 + 12 =Add the ones
then add the tens
How to...Step 1:Step 2:Step 3:
Back to
Instruction
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Average
3 + 4 + 2 = 9
= 9 3 = 3
The value/amount of each item when the total is distributed
across each item equally.
Back to
Instruction
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Back to
Instruction
A fraction whose numerator or denominator or both contain fractions.
315
15
23= 3 1
5 = 15
23
15
23
Must be written as a fraction.
Complex Fraction
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Used to make operations with fractions easier. Divide the numerator of one fraction and the denominator of another fraction by their GCF.
15
1520+
=3201+1
51520+
1
3
GCF of 5 and 15 is 5.
Back to
Instruction
Cross Simplify
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Back to
Instruction
Distributive Property
5
(3 + 2)3
3x5=3(3+2)2(3+4)=(2x3)+(2x4)
23 4
a(b+c)=ab+ac
Multiplying a sum by a number is the same as multiplying each addend in the sum by the
same number and then adding the products.
a(b-c)=ab-ac
also applies to subtraction
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Dividend
24 ÷ 8 = 32483
248 = 3
Dividend Dividend
Dividend
The number being divided in a division equation.
Back to
Instruction
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Divisor
2483 25
8 = 3R1
Divisor Divisor
The number the dividend is divided by. A number that divides
another number without a remainder.
Must divide evenly.
Back to
Instruction
24 ÷ 8 = 3
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Back to
Instruction
101 10=
Power of 10
Any integer powers of the number ten. (Ten is the base, the exponent is the power.)
102 100= 103 1,000=
10x10 =10 = 10x10x10 =
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Back to
Instruction
ProfitThe difference between the amount
earned and the amount spent.
EarnedSpentProfit
-______$30 Washing
Cars
$12-______
$18Supplies
Profit
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Back to
Instruction
Quotient
The number that is the result of dividing one number by another.
12 ÷ 3 = 4Quotient 12
4 3
Quotient 12 4 3 =Quotient
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Reciprocal
One of two numbers whose product is one.
1 x 1 = 11 is the
reciprocal of 1.
2 x 12 = 1
Number
Reciprocal
r x r = 1
Back to
Instruction
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Back to
Instruction
Repeating Decimal
A decimal with a digit or group of digits that repeats endlessly.
3 1.0.3
9-___1
30
0___9-
1
03
09___-1
...
13
= .3__ 7
33= .21
__
(.212121...)
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Back to
Instruction
Terminating Decimal
A decimal that ends and doesn't go on forever.
3 1.0.3
9-___1
30
0___9-
1
03
09___-1
...
1/2 = .5 3/8 = .375
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Back to
Instruction
Vertical
In an up-down position.ve
rtic
al
horizontaldiagonal
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Standards for Mathematical Practice
MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.
Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.
If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.
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Standards for Mathematical Practice
MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.
Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.
If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.
[This object is a pull tab]
Mat
h Pr
actic
e
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