unit 4 fractions ccm6 and ccm6+ 2015-16 name...

CCM6/6+ Unit 4 Fractions Packet page 1

UNIT 4 – FRACTIONS

CCM6 and CCM6+

2015-16

NAME____________________________

TEACHER _________________________

Estimated Test Date ________________

Main Ideas Pages

Unit 4 Vocabulary 2

Review Fraction Basics

writing fractions from pictures

mixed numbers/improper fractions

equivalent fractions

simplifying fractions

TI-73 calculator fraction keys

3-7

Add and Subtract Fractions without renaming/borrowing 8-9

Subtract Fractions with renaming/borrowing 10-12

Multiply Fractions 13-18

Divide Fractions 19-23

Mixed Operation Problem-Solving with Fractions 24-25

Study Guide 26-29

http://cmapp.wcpss.net/uploads/files/ms_math_2014-15/6th_grade/unit_4/day35-36_mixedreviewfractionsproblemsolving_ccm6_unit_4.docx


Unit 2 Vocabulary

denominator the bottom number of a fraction that tells how many equal parts are in the whole

difference the answer to a subtraction problem

dividend the number that is divided

divisor the number that you divide by

fraction a number in the form a/b, where b≠0

improper fraction a fraction in which the numerator is greater than or equal to the denominator

mixed number an integer that is not zero and a fraction

numerator the top number of a fraction that tells how many parts of a whole are being considered

product the result when two or more numbers are multiplied

quotient the answer to a division problem

reciprocal The multiplicative inverse of a number

simplest form a fraction is in simplest form when the numerator and denominator have no common factors other than 1, also known as lowest terms or reduced form

sum the answer to an addition problem


ADDING and SUBTRACTING Fractions...Review

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You always must __________________ ______________________...this means

you

have a.... must be sure to multiply both fractions values that will make the

DENOMINATORS the SAME.

And your answer Change these answers so that they are PROPER and SIMPLIFIED:

must be: 9

6

13

10

12

9

1) PROPER

2) SIMPLIFIED

Another good idea... ESTIMATE to see if your answer makes sense!

Compare each fraction to 0, ½, or 1.

Practice:

3

4+

1

3

3

4+

1

3

14

5−

11

15 1

4

5−

11

15

#10 is weird...why?


Subtracting with Borrowing

Two situations:

1) Whole – fraction or mixed #

a) 8 − 3

5 Draw it: 8 −

3

5

b) 6 − 32

3 Draw it: 6 − 3

2

3

2) Mixed # - Mixed # Change it...83

11 becomes 7

3+11

11 =

51

8 becomes

Don’t forget common denominators!

71

3 8

2

5 9

2

9

− 51

2 −4

9

10 −6

1

3


Multiply Fractions with Pictures


Multiply Fractions Notes

Yippee...

I don’t need a ________________________ _____________________________

Instead, I get rid of 8 becomes

whole numbers...

6 becomes

12

3 becomes

73

5 becomes

If you cancel... it becomes a lot easier!

(÷ 𝑡𝑜𝑝𝑠 𝑎𝑛𝑑 𝑏𝑜𝑡𝑡𝑜𝑚𝑠)

My answer still must be: _______________________ and _______________________

Practice Problems

7

8 •

4

5

5

12 •

9

10

12 • 5

6

18 • 7

9

32

3 •

9

11

21

2 • 1

1

5

I ate 3

5 of the pie. If the pie had 10 slices, how many slices are left?


𝟏

𝟑


Multiplying Fractions Application

1. Alisa had 1

2 a liter of juice in a bottle. She drank

3

4 of the juice that was in the

bottle. How many liters of juice did she drink?

2. Kendra is making 1

2 of a recipe. The full recipe calls for 3

1

4 cup of flour. How

many cups of flour should Kendra use?


3. A recipe for chocolate chip cookies makes 4 dozen cookies and calls for the

following ingredients:

1 1

2 C margarine

13

4 C sugar

2 tsp vanilla

31

4C flour

1tsp baking powder

1

4 tsp salt

8 oz chocolate chips

a. How much of each ingredient is needed for 12 dozen cookies?

b. How much of each ingredient is needed for 2 dozen cookies?

4. The distance between Rosa’s house and her school is 3

4 mile. She ran

1

3of the

way to school. How many miles did she run?


5.

CCM6/6+ Unit 4 Fractions Packet page 19 Dividing...First let’s use pictures

Sometimes a picture helps you divide...other times it doesn’t.


Fraction division with circles:

A. Janie has 2 ½ pies. She wants to give ¼ of a pie to each of her friends. How many

friends will get pie?

First: Draw circles to show 2 1/2.

Second: Convert your picture to show fourths not halves.

Dividend:_____________ Divisor: ______________ Quotient: ______________

B. Charlie has 6 SlimJims. He wants to give each friend 2/3 of a SlimJim. How many

friends will get a piece?

First: Draw 6 circles.

Second: Convert your picture to show thirds. Circle every 2/3—be sure you combine

the extra pieces, too!



Fraction division with number lines:

C. Billy Bob has 3 ¾ hours left to complete his project. If he works ¾ of an hour each

day, how many days will it take to complete the project?

First, mark the wholes from 0 to 4. Mark four equal parts between each whole—this

means 3 marks inside the space for each whole.

Second: Jump ¾ at a time by drawing a “jump.” Count how many jumps it took to get

to 3 ¾.


D. It takes Suzie 6 hours to mow her large yard. If she plans to drink a bottle of water

every 3/5 of an hour, how many bottles of water will she drink?

First, mark the wholes from 0 to 6. Split each whole into five equal parts (this means you

need to make four marks inside the space of each whole).

Second: Jump 3/5 at a time by drawing “jumps.” Count how many jumps it took to get

to 6.


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Summary: How do pictures help me divide with fractions?

Which method(s) do I like best?


Fraction Division Notes

Let’s see if you can find a pattern with your calculator... fill in the answers and look for a pattern!

8 ÷1

2

This is the same as what math problem?

10 ÷1

3

same as?

5 ÷1

4

same as?

8 ÷2

3

same as?

12 ÷3

4

same as?

What did the whole number do with the numerator? ________________________________________

What did the whole number do with the denominator? _______________________________________

Fraction division is multiplying by the ________________ of the _____________ fraction...

Rhyme:

_________________ fraction, don’t be shy,

________________ yourself and multiply!

Now set these up and divide! You can draw a picture to solve #1 and 3.

1) 11

3 ÷ 4 2) 2

1

4 ÷ 1

1

2 3) 8 ÷ 1

1

3


Mixed Review for Fraction Operations using Problem Solving

1. Steven says “I would rather have 5/9 of $72 than 4/6 because I will get more to spend.” Is he

correct?

2. A pan of brownies was left out on the counter and 1/4 of the brownies were eaten. Then you came along and ate 2/3 of the brownies that were left. How much of the whole pan of brownies was eaten?

3. You have 6 donuts and you want to give 2/3 of them to a friend and keep 1/3 for yourself. How many donuts would your friend get? That is, how much is 2/3 of 6?

4. Mrs. Smith's class is making vests. Each vest uses 2/3 of a yard of fabric. How many vests can they make out of 18 yards of fabric?

5. A rectangle measures 4 2/3 x 3 3/7 inches. What is its area? Give your answer as a simplified mixed number or as a whole number.

6. Your class had a pizza party. 3/8 of one pizza was left over, and 4/8 of another pizza was left over. You put them both into one box. How much pizza do you have altogether?

7. A cake recipe requires 3/5 cup of sugar for the frosting and 1/5 cup of sugar for the cake. How much sugar is that altogether?

8. You walk 3/10 of a mile to your friend’s house, and then 1/2 of a mile to school. How far did you walk altogether?


9. After a party, 5/8 of the cake is left over. That night, big brother eats 1/3 of the cake that was left. How much is left over after that?

10. You have 7 5/8 feet of yarn to make a bracelet. You only use 4 1/8 yards for the bracelet. How much yarn is left over?

11. Jamar is trying to fit his encyclopedia on a shelf. Each book in his encyclopedia is 2¼ inches thick. The self is 2¼ feet wide. How many books will Jamar be able to fit?

12. The Hubba Bubba Bubble Gum Tape is 6 feet long. How many 2¼ inch pieces can the tape be cut into?

13. My garden is planted with flowers. 5/6 of the flowers are roses. 2/3 of the roses are yellow and the rest are red. What fraction of the roses are red?

14. Chris has a 3 ½ feet long board of wood. He needs to cut out 4 pieces that are each 2/3 foot long. Find the combined length of the 4 pieces. Does he have enough wood?

15. Maria needs ¾ of a cup of sugar for one serving of her recipe. How many cups of sugar will she need for 5 servings?


STUDY GUIDE Unit 4 Fractions CCM6 and CCM6+

1. What is 1/2 of HOMEWORK?

A. OM B. H C. HOM D. HOME


A. ME B. ORK C. HOM D. HOME

3. What is 1/3 of SCHOOL?

A. HOOL B. SCH C. OL D. S


A. MEWORK B. HOME C. MEW D. ME

5. What is 2/3 of SCHOOL?

A. OOL B. SC C. CHOO D. SCHOOL

For #6-8, reduce these fractions. Remember your divisibility rules???

6. 20

18 7.

32

16 8.

55

20

For #9-11, change mixed to improper or improper to mixed.

9. 8

71 = 10.

6

19 = 11.

4

35 =

For #12-22, Solve. Your answer must be simplified and proper!

12) 16

5+

8

7=_____ A)

16

31 B)

24

12 C)

8

2 D)

16

12

13) 5

3-15

1=_____ A)

15

8 B)

15

10 C)

5

1 D)

15

2

14) 3-9

2=_____ A)

9

1 B)

9

23 C)

9

72 D)

9

71


15) 4 6

5- 3

5

2=_____ A)

30

131 B)

30

137 C)

30

31 D)

30

13

16) 6

5+2

9

4=_____ A)

2

12 B)

15

92 C)

18

53 D)

5

33

17) 3

2

6

11 =____ A.

18

14 B.

9

7 C.

18

2 D.

9

11

18) 3

22

8

7 =___ A.

24

82 B.

8

21 C.

24

56 D.

3

12

19) 6

11

4

12 =___ A.

10

23 B.

24

12 C.

8

52 D.

8

21

20) 45

3 =_______ A.

20

3 B.

5

12 C.

5

22 D.

12

1

21) 100

3

10

3 =_____ A.

10

1 B.

30

300 C. 10 D.

1000

9


22) 2

1210 =_______ A. 25 B.

2

50 C. 4 D.

5

20

Solve the word problems—your answers must be simplified and proper!

Underline numbers and circle words that mean math!

23) Jamie needs 2 ¾ yards of fabric to make a costume. She has 12 yards of fabric. How much fabric will

be left after she makes the costume?

24) The track around Martin is ¼ of a mile long. Mr. Castro ran 12 miles. How many laps did he run?

25) A cereal box contains 91

4 cups of Choco-Crunchies. This is your FAVORITE cereal! You PIG OUT at

breakfast and eat 52

3 cups of cereal. How much cereal is left in the box?

26) Draw a picture to show 4 • 2

3. You can use circles or number lines.

27) Draw a picture to show 4 ÷ 2

3. You can use circles or number lines.


28) Kendrick has 7

8 of a candy bar. His friend, Davis, ate

2

3 of Kendrick’s candy bar.

a) How much of the candy bar did Davis eat?

b) How much of the candy bar does Kendrick have left?

29) Michael spent 31

3 hours studying in the morning and 2

3

4 hours studying in the evening.

a) What was the total time he spent studying? ________ hours

b) How much longer did he spend studying in the morning than in the evening? _______ hour

30) What do you need to study the most about fractions to be ready for the test?

unit 4 fractions ccm6 and ccm6+ 2015-16 name...

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