CCM6/6+ Unit 4 Fractions Packet page 1

UNIT 4 – FRACTIONS CCM6 and CCM6+ 2016-2017 NAME____________________________ TEACHER _________________________ Estimated Test Date ________________ Estimated Quiz Date ________________ Pages

Main Ideas Unit 4 Vocabulary

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Review Fraction Basics  writing fractions from pictures  mixed numbers/improper fractions  equivalent fractions  simplifying fractions  TI-73 calculator fraction keys Adding and Subtracting Fractions without renaming/borrowing

3-7

8-9

Subtracting Fractions with renaming/borrowing

10-12

Multiplying Fractions

13-18

Dividing Fractions

19-23

Mixed Operation Problem-Solving with Fractions

24-25

Unit 4 Study Guide

26-28

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Unit 4 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

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ADDING and SUBTRACTING Fractions...Review ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ You always must have a

__________________ ______________________...this means must be sure to multiply both fractions values that will make the DENOMINATORS the SAME.

And your answer must be:

Change these answers so that they are PROPER and SIMPLIFIED:

9

13

12

6

10

9

1) PROPER and 2) SIMPLIFIED

Another good idea... sometimes using ESTIMATION helps to see if your answer makes sense! Compare each fraction to 0, ½, or 1. (This doesn’t work well for all fractions!)

Practice: 3

+ 4

4

1

3

+ 4

3

15 −

Work it out:

11 15

4

1 3

15 −

11 15

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***Question 10 on this page is weird...why?

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Subtracting with Borrowing (Regrouping) Two situations: 1) Whole – fraction or mixed #

3

3

a)

8−5

Draw it: 8 − 5

b)

6 − 33

2

2

Draw it: 6 − 3 3

3

2) Mixed # - Mixed #

3+11 11

Change it...811 becomes 7

=

1

58 becomes Don’t forget common denominators! Practice:

7

1 3

−5

1 2

8

2

−4

9

9

5

−6

10

11

2 9 1 3

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Multiply Fractions with Pictures

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Multiplying Fractions: Notes Yippee! I don’t need a…….. Instead, I get rid of

_______________

8

becomes

6

becomes

________________________

whole numbers...

1 7

2 3 3 5

becomes

becomes

If you cancel... (÷ 𝑡𝑜𝑝𝑠 𝑎𝑛𝑑 𝑏𝑜𝑡𝑡𝑜𝑚𝑠)

it becomes a lot easier!

My answer still must be:

_________________ and _________________________

Practice Problems

1)

7 4 • 8 5

3) 12 •

2)

5

4) 18 •

6

2

9

3

11

5) 3 •

5 9 • 12 10

6) 2

14

7 9

1 1 •1 2 5

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

𝟏 𝟑

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Multiplying Fractions Application 1

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1. Alisa had a liter of juice in a bottle. She drank of the juice that was in the 2 4 bottle. How many liters of juice did she drink?

1

1

2. Kendra is making of a recipe. The full recipe calls for 3 cup of flour. How 2 4 many cups of flour should Kendra use?

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3. A recipe for chocolate chip cookies makes 4 dozen cookies and calls for the following ingredients: 1



1 C margarine



1 C sugar



2 tsp vanilla



3 C flour



1tsp baking powder

 

2

3 4

1 4

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?

3

1

4. The distance between Rosa’s house and her school is mile. She ran of the 4 3 way to school. How many miles did she run?

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Dividing Fractions...First let’s use pictures

Sometimes a picture helps you divide...other times it doesn’t. 19

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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! Dividend:_____________

Divisor: ______________

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Quotient: ______________

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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. Dividend:_____________

Divisor: ______________

Quotient: ______________

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. Dividend:_____________

Divisor: ______________

Quotient: ______________

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

Summary: How do pictures help me divide with fractions? Which method(s) do I like best? 21

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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

This is the same as what math problem?

2

10 ÷ 5÷

1

8÷

2

1

same as?

3 same as?

4 same as?

3

12 ÷

3

same as?

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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 & 3 1) 1

1 3

÷4

2) 2

1 4

÷1

22

1 2

3) 8 ÷ 1

1 3

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Mixed Operation Problem-Solving with Fractions 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?

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CCM6/6+ Unit 4 Fractions Packet page 25 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?

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Unit 4 STUDY GUIDE (CCM6 and CCM6+) For #1-3, reduce these fractions to simplest form. (Remember your divisibility rules???) 1.

18 20

2.

16 32

3.

20 55

For #4-6, change mixed to improper or improper to mixed. 7 8

4. 1 =

5.

19 = 6

6. 5

3 = 4

For #7-17, Solve. Your answer must be simplified and proper! 7)

5 7 + = _____ 16 8

8)

3 1 = _____ 5 15

9) 3 -

10) 4

11)

12)

2 =_____ 9

A) 1

3 16

C)

2 8

D)

12 16

10 15

C)

1 5

D)

2 15

8 15

B)

A)

1 9

B) 3

A) 1

5 4 + 2 = _____ 6 9

= ____

12 24

A)

5 2 - 3 =_____ 6 5

1 2 1  6 3

B)

A.

13 30

A) 2

14 18

2 9

C) 2

B) 7

1 2

B.

13 30

B) 2

7 9 26

7 9

D) 1

C) 1

9 15

C.

3 30

C) 3

2 18

7 9

D)

5 18

D. 1

D) 3

1 9

3 5

13 30

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13)

14)

1 1 2 1 4 6

3 4 5

=___

= _______ A.

3 3  15) 10 100 =_____

16)

10  2

A. 3

1 2

A.

=_______

2 10

B. 2

1 24

C. 2

5 8

D.

21 8

2 5

D.

1 12

D.

9 1000

3 20

B.

12 5

C. 2

1 10

B.

300 30

C. 10

A. 25

B.

50 2

C. 4

D.

20 5

Word Problems. Your answers must be simplified and proper! 17) 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?

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

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19) A cereal box contains 9 cups of Choco-Crunchies. This is your FAVORITE 4

2

cereal! You PIG OUT at breakfast and eat 5 cups of cereal. How much cereal is 3

left in the box?

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20) Draw a picture to show 4 • . You can use circles or number lines. 3

2

21) Draw a picture to show 4 ÷ . You can use circles or number lines. 3

7

2

8

3

22) Kendrick has of a candy bar. His friend, Davis, ate 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?

1

3

3

4

23) Michael spent 3 hours studying in the morning and 2 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 28