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MidTerm Review 2017.notebook
1
October 09, 2017
Oct 67:50 AM
Mid-Term Study Guide Review
Oct 43:50 PM
Oct 68:18 AM
Fraction Word Problems
fractionwordproblems.ppt
Oct 43:51 PM
Oct 43:52 PM Oct 68:45 AM
FractionDecimalsPercentsPPT.pptx
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MidTerm Review 2017.notebook
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October 09, 2017
Oct 43:52 PM Oct 43:52 PM
Oct 43:53 PM Oct 43:53 PM
Oct 43:56 PM Oct 43:56 PM
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MidTerm Review 2017.notebook
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October 09, 2017
Oct 43:56 PM Oct 43:58 PM
Oct 43:58 PM
21. A weight-lifter's maximum amount he can lift is 300 pounds. Write and solve an inequality to find the number of 50-pound weights he can possibly lift.
Oct 43:59 PM
Oct 43:59 PM Oct 43:59 PM
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MidTerm Review 2017.notebook
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October 09, 2017
Oct 44:00 PM Oct 44:00 PM
Oct 99:43 AM
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Attachments
Fraction Check.docx
fractionwordproblems.ppt
FractionDecimalsPercentsPPT.pptx
1)
2)
3)
4)
SMART Notebook
Fraction Word
Problems
M/J Math 1
EETT Lesson #6
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
When reading word problems containing fractions,
certain phrases can indicate the operation that you need to do in order to solve the word problem.
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Subtraction −
“How much more is needed?”
“How much further than?”
“How much is left?”
“How bigger than?”
Addition +
“How much together?”
“How far will she travel
from home to the park,
then to the library?”
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Division ÷
“Find the quotient…”
“Divided into to pieces…”
“How many will fit?”
“How many can be split from?”
Multiplication ×
“Times longer...”
“The product of…”
“A fraction of something…”
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
In the recent Student Government elections, Larry received of the votes for treasurer and Leah received of the votes.
What fraction of the votes did both candidates earn together?
1
3
1
15
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Solution:
×5
=
+
×5
=
+
=
=
1
15
1
3
1
15
5
15
5+1
15
6
15
2
5
Together they received of the votes.
2
5
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
One tree is 6 feet tall. Another one is only 3 feet tall. How much taller is the larger of two trees.
1
4
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Solution:
=
− 3
6
5
2
1
4
4
4
3
4
1
4
The larger tree is
feet taller than the smaller one.
2
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Sean swam 2 miles at swim team practice. If Becky swam 1 times as far as Sean, then how many miles did Becky swim?
1
3
1
2
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Solution:
2
×
=
×
=
=
1
3
=
3
7
3
1
2
Becky swam
miles at swim
team practice.
3
1
2
3
2
1
3
21
6
3
6
1
2
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Charlie works at a livery and uses a 60 pound bag of oats to feed the horses. If each horse gets
pounds of food, then how many horses can Charlie feed with one bag of oats?
4
5
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
Solution:
60
÷
=
×
=
=
75
÷
=
One bag of oats can feed 75 horses.
4
5
5
4
60
1
300
4
4
5
60
1
Math 2: 6-6 Dividing Fractions & Mixed #’s
Sunshine State Standards: MA.A.3.3.1-1, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-2
SMART Notebook
and Percents
Learning to Juggle
with:
Decimals,
Fractions,
I juggled
Granny’s china
teacups…
once!
A Bundled Unit
© Created by Mike Walker
Introduction
Not that kind of introduction, big fella!
Hi!
My name’s Sparky!
Fractions, Decimals, and Percents
Fractions, decimals, and percents are different ways of
representing the same number.
= 0.5 = 50%
These numbers look different, but they all have the exact same value.
Fraction Decimal Percent
Hopefully, you just had an off day!
Fractions, Decimals, and Percents
Because we use fractions, decimals, and percents in everyday life, it’s helpful if we can juggle or change between each form…
…making these
numbers easier
to understand.
I understand
that ¼ pound of cheesy bacon burger is good!
I don’t understand how I got a 25% on my last math test.
Fractions, Decimals, and Percents
When do we use
Decimals?
Sports
0.375 – baseball
batting average
Prices
$299.99
Gas Quantities
18.8959 gal
Pi
3.141592…
What are some other decimal uses?
Fractions, Decimals, and Percents
When do we use
Percents?
Grades
25%
Thanks
for reminding me!
Retail Sales
60% off!
Tipping Rates
15% to 20%
Statistics
100% of students choose
shorter school days!
Where else do we find percentages?
0.25
110%
40%
Changing Decimals to Percents
Part 1:
Pondering the Percent
A percent represents
an amount out of 100.
So, for example,
instead of saying Sparky
got 25 out of 100 on his last
math test, we say Sparky got a 25%.
We use the (%) symbol instead of writing fractions with a denominator of 100.
Why
does this
number haunt me?
Decimals to Percents
Because a percentage represents
an amount out of 100, to turn a decimal into a percent, all we do is
multiply the decimal by 100.
Let’s change 0.62 to a percent!
100
× 0.62
200
+ 600
62.00
= 62
Don’t forget the percent sign!
62%
Decimals to Percents
Someone
told me that when
you multiply by 100, it’s
just like moving the
decimal point 2 places
to the right!
That someone was right!
Moving
the decimal
seems waaaaay easier to me!
It is! Just don’t forget to add the percent sign after you move the decimal!
Got it!
Decimals to Percents
So, let’s use Sparky’s method to easily change some decimals into percents.
0.45
= 45%
→ 45.0
0.7
Before we can move the decimal 2 places to the right, we have to add a zero.
Example 1:
Example 2:
0
→ 70.0
= 70%
00
Decimals to Percents
Example 3:
1.25
→ 125.0
= 125%
Example 4:
2
An “understood” decimal comes after the 2.
.
Add two zeros so we can move the decimal!
→ 200.0
= 200%
I’m pretty sure I have this!
We better practice just in case!
Decimals to Percents
Change the following decimals into percents.
1) 0.75
2) 0.11
3) 0.8
4) 0.333
5) 1.45
= 75%
= 11%
= 80%
= 33.3%
= 145%
6) 0.2
7) 0.615
8) 4
9) 0.5
10) 0.99
= 20%
= 61.5%
= 400%
= 50%
= 99%
Part 2:
Changing Percents back to Decimals
I’m getting dizzy!
This won’t be bad. Trust me!
Percents to Decimals
If we move the decimal 2 places to the right to change a decimal to a percent, what do you suppose we do to change a percent back to a decimal?
Move the
decimal 2 places
to the left?
Pure genius!
It
runs in the
family!
Check this out, Professor!
%
%
Percents to Decimals
Example 1:
85
Locate the “understood” decimal after the 5 and remove the percent sign.
%
.
Then, move the decimal 2 places to the left.
→ .85
= 0.85
Example 2:
30
.
→ .30
= 0.3
Example 3:
115
.
= 1.15
Your turn!
Percents to Decimals
Change the following percents into decimals.
1) 18%
2) 100%
3) 5%
4) 12.9%
5) 88%
6) 7.43%
7) 150%
8) 11%
9) 316.2%
10) 7.7%
= 0.18
= 1
= 0.05
= 0.129
= 0.88
= 0.0743
= 1.5
= 0.11
= 3.162
= 0.077
Part 3:
Changing Decimals to Fractions
Head…
going…to…
explode!
Stay with me Sparticus!
When do we use
Fractions, Decimals, and Percents
Fractions?
Cooking/Recipes
cups flour
Measuring Length
inches
Telling time
after four
(a quarter after four)
Reading Music
note
Can you think of other ways we use fractions?
19
Focusing on Fractions
A fraction is formed by two numbers; a top number, the numerator, over a bottom number, the denominator.
or
→
→
Proper fractions, like this one, represent numbers less than 1.
Decimals to Fractions
Before we start changing decimals into fractions, we need a good understanding of how to properly say decimals.
Believe it or not, when you
properly say a decimal,
you are automatically
creating the fraction.
I’ll believe
it when I see it…
or hear it!
At least the crazy face is gone!
Decimals to Fractions
0. 3927
(Sample number)
Can you name the following decimal place values?
tenths
hundredths
thousandths
ten thousandths
Now let’s try to properly
“say” some decimals?
Decimals to Fractions
Practice saying the following decimals to yourself:
1) 0.7 →
2) 0.23 →
3) 0.034 →
4) 9.8 →
say “seven tenths”
say “twenty-three hundredths”
say “thirty-four thousandths”
say “nine and eight tenths”
Decimals to Fractions
1) 0.8
3) 0.052
=
=
2) 0.16
4) 4.4
=
= 4
What work still needs to be done with all of these fractions?
If you said “simplify,” you’re right!
As you say each decimal, think about the fraction you’re saying to yourself:
Decimals to Fractions
1) 0.8
2) 0.16
=
=
3) 0.052
4) 4.4
=
= 4
Simplify.
=
=
=
= 4
I get it!
But I better
do some more practice.
I like your attitude!
Change the following decimals into fractions.
Decimals to Fractions
Don’t forget to simplify!
1) 0.2
2) 1.32
3) 0.124
4) 0.5008
=
= 1
=
=
=
= 1
=
=
Changing Fractions to Decimals
1
Part 4:
Fractions to Decimals
Decimals are related to fractions because they also represent numbers
less than 1.
Does anyone know how to turn a
fraction into a decimal?
If you said to divide
the numerator by the denominator, you’re right!
But how
does that give you a decimal?
Check this out!
Fractions to Decimals
Let’s use as an example.
To turn into a decimal, we divide the numerator, 3, by the denominator, 4.
3.0
4
-2 8
2
0
0
.
0
7
5
-20
0
So 0.75
Hint: you can think of a fraction bar like a division (÷) symbol.
Fractions to Decimals
Can someone guess what the decimal form of would be?
If you said 3.75, you’re right! Notice how the whole
number stays the
same in both forms.
I think
I get it, but can
we do one more
to be sure?
Absolutely!
Fractions to Decimals
Let’s change into a decimal!
Remember! The whole number will stay the same, so we just need to divide 2 by 3.
2.0
3
0
.
6
-1 8
0
2
0
6
-18
2
0
0
At this point, you can see the division problem will never end, and the 6 will keep repeating.
So 5.6
I’m
still iffy!
Let’s practice!
= 0.3
= 1.5
= 2.6
= 9.625
Fractions to Decimals
Change the following fractions into decimals.
1)
2)
3)
4)
5)
6) 1
7) 2
8) 9
= 0.25
= 0.4
= 0.83
= 0.7
SMART Notebook
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