Topic 12 Adding and Subtracting Fractions and Mixed Numbers …s3.amazonaws.com/scschoolfiles/249/topic_12_adding… · · 2013-06-122007-02-07 · Topic 12 Adding and Subtracting

Topic 12

Adding and Subtracting Fractions and Mixed Numbers with Like

Denominators

Exam Intervention Booklet

Materials crayons or markers

Nur wove 2 __ 5 of a rug in February and 1 __

5 of it in March.

Find what part of the rug she has finished in all by

answering 1 to 4.

1. Color 2 __ 5 of the rectangle on the right.

2. Color 1 __ 5 more of the rectangle on the right.

3. How much of the rectangle

did you color in all?

____

This is the sum of 2 __ 5 and 1 __

5 . So, 2 __

5 � 1 __

5 � 3 __

5 .

4. What part of her rug has Nur finished in all?

Jamal wove 2 __ 6 of a rug in February and 2 __

6 in March.

Find what part of the rug he has finished in all by

answering 5 to 11.


6. Color 2 __ 6 more of the rectangle on the right.

7. How much of the rectangle

did you color in all?

____

8. What is 2 __ 6 � 2 __

6 ?

9. What is a fraction equivalent to 4 __ 6 ,

but with smaller numbers? Color

the second rectangle to find out. 4 __ 6 � ____

10. So, 2 __ 6 � 2 __

6 � 4 __

6 � ____ .

11. What part of his rug has Jamal finished in all?

Intervention Lesson H36 155

Math Diagnosis and Intervention SystemIntervention Lesson H36

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Adding Fractions with Like Denominators

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12. Reasoning Explain how to add 1 __ 9 � 4 __

9 .

Add.

13. 1 __ 3 1 __

3

14. 1 __ 5 3 __

5

1 __ 3 � 1 __

3 � 1 __

5 � 3 __

5 �

15. 1 __ 4 2 __

4

16. 1 __ 6 1 __

6 1 __

6 1 __

6 1 __

6

1 __ 4 � 2 __

4 � 2 __

6 � 3 __

6 �

17. 2 __ 8 � 5 __

8 � 18. 3 ___

10 � 2 ___

10 � �

19. Calvin bought a gallon of yogurt. He ate 1 __ 6 gallon

the first day, and 2 __ 6 gallon the second day.

What fraction of the yogurt did he eat?

20. Three-fifths of Mr. James’ class are wearing blue jeans

and white shirts. One-fifth of the class are wearing blue

jeans and red shirts. One-fifth of the class are wearing

brown pants and white shirts. What fraction of Mr. James’

class are wearing white shirts?

21. Reasoning What fraction would you add to 1 __ 3 to get 3 __

3 ?

156 Intervention Lesson H36

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Adding Fractions with Like Denominators (continued)

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Subtracting Fractions with Like Denominators

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Materials crayons or markers

Tammy loves tuna bake. When she came home from school, she

found 6 __ 8 of a tuna bake on the stove. She ate 1 __ 8 of it. Find how

much of the tuna bake was left by answering 1 to 5.


2. Cross out 1 __ 8 of the part you colored.

3. How much of the rectangle you colored is not crossed out? ____

4. What is 6 __ 8 � 1 __ 8 ? ____

5. How much of the tuna bake was left after Tammy ate?

Brad found 3 __ 4 of a submarine sandwich when he came home

from school. He ate 1 __ 4 of the sandwich. Find how much of the

sandwich was left by answering 6 to 12.


7. Cross out 1 __ 4 of the part you colored.

8. How much of the rectangle you colored is not crossed out? ____

9. What is 3 __ 4 � 1 __ 4 ? ____

10. What is a fraction equivalent to 2 __ 4 , but with smaller numbers? Color the second rectangle to find out. 2 __ 4 � ____

11. So, 3 __ 4 – 1 __ 4 � 2 __ 4 � ____ .

12. How much of the sandwich was left after Brad ate?

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13. Reasoning Explain how to subtract 5 ___ 10 � 2 ___ 10 .

Subtract.

14. 1 __ 6 1 __ 6 1 __ 6 1 __ 6 1 __ 6

15. 1 __ 5 1 __ 5 1 __ 5

5 __ 6 � 3 __ 6 � 3 __ 5 � 1 __ 5 �

16. 1 __ 4 1 __ 4 1 __ 4

17. 1 __ 5 1 __ 5 1 __ 5 1 __ 5

3 __ 4 � 1 __ 4 � 4 __ 5 � 2 __ 5 �

18. 4 __ 7 � 3 __ 7 � 19. 5 __ 9 � 4 __ 9 �

20. 7 __ 8 � 1 __ 8 � � 21. 4 __ 6 � 1 __ 6 � �

The table shows the distances run by members of a track team. Use the table for Exercises 22 and 23. Runner

Distancein miles

Rosie 7 __ 8

Tricia 4 __ 8

Amy 5 __ 8

Caro 6 __ 8

22. How much farther didRosie run than Tricia?

23. How much farther did Caro run than Tricia?

24. Reasoning Why would it be more difficult

to subtract 2 __ 3 � 1 __ 6 than 2 __ 3 � 1 __ 3 ?


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Subtracting Fractions with Like Denominators (continued)

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Adding and Subtracting Fractions with Like Denominators

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Carlos spent 3 __ 4 hour writing email and another 3 __

4 hour surfing the internet.

How much time did he spend on his computer in all?

Find 3 __ 4 � 3 __

4 by answering 1 to 4.

1 1

1 __ 4 1 __

4 1 __

4 1 __

4 1 __

4 1 __

4

1. Show 3 __ 4 � 3 __

4 with fraction strips.

2. What is 3 __ 4 � 3 __

4 ?

3. Use the fraction strips to find 6 __ 4 as a mixed 1 1

1 __ 4 1 __

4 1 __

4 1 __

4 1 __

4 1 __

4

1 1 __ 2

number in simplest form.

3 __ 4 � 3 __

4 � 6 __

4 � 1 ____

4 �

4. How much time did Carlos spend on his computer in all?

5. Reasoning Explain how to find 7 ___ 10

� 9 ___ 10

.

Connie had 5 __ 6 hour to surf the internet. She finished with

one site in 1 __ 6 hour. How much time did she have left?

Find 5 __ 6 � 1 __


6. Show 5 __ 6 with fraction strips.

7. Take away 1 __ 6 .

8. What is 5 __ 6 � 1 __

6 ?

9. Write the difference in simplest form. 4 __ 6 �

10. So, 5 __ 6 � 1 __

6 � 4 __

6 � .

11. How much time did Connie have left to surf the internet?

1

1 __ 6 1 __

6 1 __

6 1 __

6

1 __ 3 1 __

3

1

1 __ 6 1 __

6 1 __

6 1 __

6 1 __

6


12. Reasoning Explain how to find 7 __ 8 � 1 __

8 .

Add. Write the sum in simplest form.

13. 5 ___ 12

� 1 ___ 12

14. 5 __ 9 � 1 __

9 15. 4 ___

15 � 8 ___

15

16. 3 __ 5 � 4 __

5 17. 6 __

7 � 4 __

7 18. 2 __

3 � 2 __

3

19. 7 ___ 10

� 9 ___ 10

20. 7 __ 8 � 5 __

8 21. 11 ___

12 � 5 ___

12

Subtract. Write the difference in simplest form.

22. 2 __ 3 � 1 __

3 23. 11 ___

12 � 1 ___

12 24. 7 __

9 � 1 __

9

25. 7 __ 8 � 1 __

8 26. 9 ___

10 � 3 ___

10 27. 3 __

4 � 1 __

4

28. Each class is making a friendship chain the length of the

school gym, for the end of year party. The fifth grade class

has 7 ___ 10

of their chain finished. The sixth grade class has 9 ___ 10

of theirs finished. How much more of the sixth grade chain

is finished than the fifth grade chain?

29. Reasoning Richard gathered 7 ___ 12

of a dozen eggs and Karina gathered

5 ___ 12

of a dozen. What part of a dozen did they gather in all? Explain.


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Adding and Subtracting Fractions with Like Denominators (continued)

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Adding and Subtracting Fractions on a Number Line

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Materials place-value blocks, for each student

Sarah walks 1___12

of the way to school. Then, she rides a bus 3__4

or 9___12

of

the way. Finally, she has to walk the rest of the way. When she gets off

the bus, what part of the way to school is she?

Find 1___12

� 9 ___ 12

by answering 1 to 4.

1. The number line below has an arrow from 0 to 1___12

to show how far

Sarah walks before she catches the bus. Draw another arrow that

is 9___12

units long, starting at 1___12

.

2. At what fraction does your arrow end?

The two arrows show that 1___12

� 9___12

� 10___12

.

3. What is 10___12

in simplest form?

4. When Sarah gets off the bus, what part of the way to school is she?

When Sarah gets off the bus, how much farther does she need to walk to get to school?

Find 12___12

� 10___12

by answering 5 to 8.

5. Draw an arrow that is 10___12

units long, from 12___12

or 1 back toward zero.

6. At what fraction does your arrow end?

The number line shows that 12___12

� 10___12

� 2___12

.


7. What is 2___12

in simplest form?

8. When Sarah gets off the bus, how much farther does she need to walk to get to school? of the way

Use the number line to add or subtract. Write answers in simplest form.

9. 3___10

� 4___10

� 10. 7___10

� 1___10

� �

11. 9___10

� 3___10

� � 12. 8___10

� 3___10

� �

13. 1__8 � 4 __

8 � 14. 3 __

8 � 1 __

8 � �

15. 7__8

� 1__8

� � 16. 5__8

� 3__8

� �

17. Rodney mixed 2__9

of a bottle of apple juice with 4__9

of a bottle

of cranberry juice. How much juice was in the mixture?

18. Reasoning What is 4__9

� 2__9

� 1__9

?


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Adding and Subtracting Fractions on a Number Line (continued)

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Adding Mixed Numbers

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Materials fraction strips

Caroline is painting the ceiling border of her room. On Saturday, she

painted 1 3 __ 4 feet. On Sunday, she painted 1 7__

8 feet. How much did she

paint in the two days combined?

Find 1 3 __ 4 � 1 7__


1. Estimate. 1 3__4

� 1 7__8

is about � � .

2. Show 1 3__4

� 1 7__8

with fraction strips.

3. Put the ones together and the fractions together. Change 3__4

to eighths.

4. How many eighths equal 3 __ 4 ? Write the number in 1 3 __

4 � 1 ____

8

� 1 7 __ 8 � 1 7 __

8

8

the box at the right.

5. Add the ones and write the sum at the right. Add

6 __ 8 and 7 __

8 and write the sum at the right.

6. Is 13 ___

8 a proper fraction?

7. Since 13 ___

8 is improper, simplify. What is 13

___ 8 as a mixed number?

8. Fill in the blank. 2 13 ___

8 � 2 � 13

___ 8 � 2 � 1 5 __

8 �

9. What is 1 3__4

� 1 7__8

?

10. How much border did Caroline paint in the two days combined?


11. Is the answer 3 5__8

close to the estimate of 4?

Since 3 5__8

is close to the estimate of 4, 3 5__8

is a reasonable answer.

Add. Write the sum as a simplified fraction.Estimate to check.

12. 2 1 __ 2

� 1 1 __ 3

13. 1 1 __ 5

� 3 3 ___ 10

14. 1 3 __ 4

� 2 __ 5

15. 2 5 ___ 12

� 3 5 __ 6

16. 6 5 __ 6

� 5 3 __ 8

17. 6 1 __ 9

� 3 2 __ 3

18. 4 3 __ 4

� 7 5 __ 6

19. 6 1 ___ 16

� 4 3 __ 8

20. 6 7__8

� 1 5__6

21. 7 1__2

� 2 3__7

22. 3 1___10

� 1 5__8

23. Ramona bought 1 2__3

pounds of strawberries,

2 1__4

pounds of apples, and 2 1__2

pounds of oranges

at the store. What was the total weight of

Ramona’s purchase?

24. Reasoning Rhonda needs 4 gallons of green paint to decorate

her room. If she mixes 2 1__3

gallons of blue paint with 1 1__2

gallons of

yellow paint, will she have enough? Explain.


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Adding Mixed Numbers (continued)

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Subtracting Mixed Numbers

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Materials fraction strips

On Monday, Carmen swam 2 3 __ 4 miles and Katie swam 1 5 __

8 miles. Answer

1 to 8 to find how much farther Carmen swam than Katie.

Find 2 3 __ 4 � 1 5 __

8 .

1. Estimate. 2 3 __ 4 � 1 5 __

8 is about � � .

2. Show 2 3 __ 4 and 1 5 __


3. How many eighths equal 3 __ 4 ? Write the number

2 3 __ 4 � 2 ____

8

� 1 5 __ 8 � 1 5 __

8

8

in the box at the right.

4. Subtract the ones and subtract the fractions. Fill in the boxes at the right.

5. What is 2 3 __ 4 � 1 5 __

8 ?

6. How much farther did Carmen swim than Katie?

7. Is 1 1 __ 8 close to the estimate of 1?

8. Is 1 1 __ 8 a reasonable answer?

On Wednesday, Carmen swam 2 1 __ 8 miles and Katie swam 1 3 __

4 miles.

Answer 9 to 18 to find how much farther Carmen swam than Katie.

Find 2 1 __ 8 � 1 3 __

4 .

9. Show 2 1 __ 8 and 1 3 __


10. What is the least common denominator of 1 __

8 and 3 __

4 ?


11. How many eighths equal 3 __ 4 ? Write the number in 2 1 __

8 � 2 1 __

8

� 1 3 __ 4 � 1 ____

8

the box at the right.

12. Compare. Write �, �, or �. 1 __ 8 6 __

8

Since 1 __ 8 is less than 6 __

8 , you need to regroup.

13. What is 1 1 __ 8 as an improper fraction?

14. What is the missing number?

2 1 __ 8 � 1 � 1 1 __

8 � 1 � ____

8

Write this number at the right.

15. Subtract the ones. What is 1 � 1? 2 1 __ 8 � 2 1 __

8 � 1 ____

8

� 1 3 __ 4 � 1 6 __

8 � 1 6 __

8

____ 8

16. Subtract the fractions. What is 9 __ 8 � 6 __

8 ?

Write 3 at the right.

17. What is 2 1 __ 8 � 1 3 __

4 ?

18. How much farther did Carmen swim than Katie on Wednesday?

Subtract. Simplify, if possible. Estimate to check.

19. 2 2 __ 3

� 1 1 __ 6

20. 2 4 ___ 10

� 1 3 __ 5

21. 5 1 __ 4

� 2 __ 5

22. 6 7 __ 8

� 1 5 __ 6

23. To make a dress, 1 1 __ 6 yards of blue material is needed and 3 __

4 yard

of red material is needed. How much more blue material is

needed than red material?

24. Reasoning If you have 7 3 ___ 16

and you subtract 3 ___ 16

, how much

do you have?


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Subtracting Mixed Numbers (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson J33

Make and Test Conjectures

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Intervention Lesson J33 103

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If a number n is a factor of a number m, what is true about the factors of n and m?

Solve by answering 1 to 5.

Start by looking at some examples and making a conjecture.

1. The table below has some examples for m and n. Notice each value of n is a factor of the value of m in the same row. Complete the table.

m Factors of m n Factors of n

12 1, 2, 3, 4, 6, 12 6 1, 2, 3, 6

28 14

24 12

36 12

36 18

2. Complete the conjecture.

If a number n is a factor of a number m, then all the factors of

are factors .

A counterexample, is an example which proves a conjecture is not true.

3. Try to find a counterexample for your conjecture. List the numbers you try.

and and and

4. Could you find a counterexample?

A counterexample can prove a conjecture is false, but it cannot prove that a conjecture is true.

5. Is your conjecture proven false? Is it proven true?

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Make and test a conjecture about the factors of n and twice n by answering 6 to 9.

6. Complete the table. Look for a pattern.

n Number of Factors of n 2n Number of Factors of 2n

6 4 12 6

14 28

12 24

40 80

7. Complete the conjecture.

The number that is twice n has more factors than n.

8. Try to find a counterexample for your conjecture. Either give the counterexample or list at least 3 sets of numbers you try.

9. Is your conjecture proven false? Is it proven true?

Write a conjecture to answer each question.

10. How are the patterns alike?

Benita’s pattern is: 2, 4, 6, 8, 10, 12, 14, …

Carol’s pattern is: 1, 3, 5, 7, 9, 11, 13, …

11. How did Beth sort the shapes Group A Group Binto Groups A and B?

12. Make another conjecture about how Beth sort the shapes.

104 Intervention Lesson J33

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Make and Test Conjectures (continued)

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Math Diagnosis and Intervention SystemIntervention Lesson J33

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Topic 12 Adding and Subtracting Fractions and Mixed Numbers …s3.amazonaws.com/scschoolfiles/249/topic_12_adding… · · 2013-06-122007-02-07 · Topic 12 Adding and Subtracting