9 15

915

93153 =

What are we going to do?

CFU

Students, you already know how to generate equivalent fractions. Now, we will use that skill to add fractions with unlike denominators.

Make Connection

We will add fractions with unlike denominators.

Learning Objective

Introduction

23

numerator

denominator

Fraction

Which fraction is equivalent to ?

Equivalent fractions are fractions that have the same value.

25

Which fraction is equivalent to ?12

=35

410

=42

102 =25

510

=55

105 =12

28

=2282 =

14

Common Core Standards 7.NS.1 - 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division

of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.

615


CFU

Students, you already know how to generate equivalent fractions. Now, we will use that skill to subtract fractions with unlike denominators.

Make Connection

We will subtract fractions with unlike denominators.

Learning Objective

Introduction

23

numerator

denominator

Fraction

1220

124204 =

Which fraction is equivalent to ?

Equivalent fractions are fractions that have the same value.

35

Which fraction is equivalent to ?12

=35

=63

153 =25

618

=66

186 =13

24

=2242 =

12




CFU

Students, you already know how to find the least common denominator of fractions. Now, we will use that skill to add fractions with unlike denominators.

Make Connection

We will add fractions with unlike denominators.

Learning Objective

Activate Prior Knowledge

The least common denominator (LCD) is the lowest multiple shared by a set of denominators.

1 1,

2 5

Find the least common denominator of the fractions below.

1. 2.

5: 5, 10, 15, 20 2: 2, 4, 6, 8, 10

2 1,

3 2

The LCD of and is 10.1

2

1

5

23

numerator

denominator

Fraction

2: 2, 4, 6, 8 3: 3, 6, 9, 12


31

2




CFU

Students, you already know how to find the least common denominator of fractions. Now, we will use that skill to subtract fractions with unlike denominators.

Make Connection

The least common denominator (LCD) is the lowest multiple shared by a set of denominators.

We will subtract fractions with unlike denominators.

Learning Objective

Activate Prior Knowledge

2: 2, 4, 6, 8

1 1,

2 3

3: 3, 6, 9, 12

Find the least common denominator of the fractions below.

1. 2.

5: 5, 10, 15, 20 2: 2, 4, 6, 8, 10

3 1,

5 2


2

1

3The LCD of and is 10.

3

51

2

23

numerator

denominator

Fraction



Concept Development

23

numerator

denominator

FractionFractions with unlike denominators have a different number of equal parts. Fractions with like denominators have the same number of equal parts. To add fractions, both fractions must have like denominators.

• To add fractions with unlike denominators use the least common denominator (LCD) to create equivalent1 fractions with like denominators.

Which pair of fractions is ready to be added? How do you know?

A

B

In your own words, how do you add fractions with unlike denominators? “To add fractions with unlike denominators ________.”

CFU

2 2

3 5

2 1

3 3

410

510

910

+ =

25

The LCD of and12

is 10.

Adding Fractions with Unlike Denominators

=+

25

12

+ =

Equivalent Fractions

22

25

410

=55

12

510

=

1 equal value

Vocabulary

Which pair of fractions is ready to be subtracted? How do you know?

A

B

In your own words, how do you subtract fractions with unlike denominators? “To subtract fractions with unlike denominators ________.”

CFU

Concept Development

23

numerator

denominator

Fraction

Subtracting Fractions with Unlike Denominators

610

510

110

- =35

12

- =

35

The LCD of and12

is 10.

Equivalent Fractions

22

35

× 610

=55

12

× 510

=

- =

Fractions with unlike denominators have a different number of equal parts. Fractions with like denominators have the same number of equal parts. To subtract fractions, both fractions must have like denominators.

• To subtract fractions with unlike denominators use the least common denominator (LCD) to create equivalent fractions with like denominators.

23

25

23

13

Skill Development/Guided Practice

1 explain2 answer to an addition problem

Vocabulary

Find a like denominator by multiplying both denominators.Create equivalent fractions with like denominators. Add fractions. Hint: Add the numerators, keep the denominator the same.

Interpret1 the sum2. “____ plus ____ equals _____.”

Add fractions with unlike denominators.1234

To add fractions, both fractions must have like denominators.

How did I/you find a like denominator? How did I/you create equivalent fractions? How did I/you add fractions?

CFU

1

2

3

2×3

1.12 +

13 =

1×32×3 +

1×23×2 =

36 +

26 =

56

2×5

2.12 +

25 =

1×52×5 +

2×25×2 =

510 +

410 =

910

6×4

3.16 +

34 =

1×46×4 +

3×64×6 =

424 +

1824 =

2224

10×3

4.3

10 +13 =

3×310×3 +

1×103×10 =

930 +

1030 =

1930

Skill Development/Guided PracticeTo subtract fractions, both fractions must have like denominators.

1 explain2 answer to a subtraction problem

Vocabulary

Find a like denominator by multiplying both denominators.Create equivalent fractions with like denominators. Subtract fractions. Hint: subtract the numerators, keep the denominator the same.

Interpret1 the difference2. “____ minus ____ equals _____.”

Subtract fractions with unlike denominators.1234

How did I/you find a like denominator? How did I/you create equivalent fractions? How did I/you subtract fractions?

CFU

1

2

3

2×3

1.12 –

13 =

1×32×3 –

1×23×2 =

36 –

26 =

16

2×5

2.12 –

25 =

1×52×5 –

2×25×2 =

510 –

410 =

110

6×4

3.34 –

16 =

3×64×6 –

1×46×4 =

1824 –

424 =

1424

3×10

4.13 –

310 =

1×103×10 –

3×310×3 =

1030 –

930 =

130

5. Sierra had of a pint of water left in her water bottle. She poured another

of a pint more water into her bottle. How much water does Sierra have?

1

4

1

2

__________________________________________________________________

Skill Development/Guided Practice (continued)

4: 4, 8, 12, 16 2: 2, 4, 6, 8

6. Theodore bought of a pound of apples and of a pound of oranges.

How much fruit did he buy?

2

3

1

5

__________________________________________________________________

1

4

1

24

4

1

11

4

2

2

2

4

1 2

4 4

3

4

3: 3, 6, 9, 12, 15 5: 5, 10, 15, 20

2

3

1

515

15

5

510

15

3

3

3

15

10 3

15 15

13

15

3

4Sierra has of a pint of water.

13

15Theodore bought of a pound of fruit

Adding Fractions

Adding Fractions

How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?

CFU

2

1

3

4

5

Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.Add fractions. Hint: Add the numerators, keep the denominators the same.

Reduce the sum, if possible.Interpret the sum. “____ plus ____ equals _____.”

Add fractions with unlike denominators.

12

3

4a

Skill Development/Guided Practice (continued)

5. Sherry bought of a pound of milk chocolate and of a pound of white

chocolate. How much more milk chocolate than white chocolate does Sherry

have?

3

4

1

2

4: 4, 8, 12, 16 2: 2, 4, 6, 8

6. Tom bought of a pound of cauliflower and of a pound of celery.

How much more cauliflower than celery did he buy?

2

3

1

5

3

4

1

24

4

1

1× ×

3

4

2

2

2

4

3 2

4 4

1

4

3: 3, 6, 9, 12, 15 5: 5, 10, 15, 20

2

3

1

515

15

5

5× ×

10

15

3

3

3

15

10 3

15 15

7

15

1

4Sherry bought ____ of a pound more ______________ than _______________.milk chocolate white chocolate

7

15Tom bought ____ of a pound more __________ than ___________.cauliflower celery

How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?

CFU

2

1

3

4

5

required = needed relevant = has to do with problemreasonableness = possible

1

2

Relevance


Adding fractions will help solve real-life problems.

There is of a pie left.

12

12

14

34

of one pie was left over after the party. There was of another pie left over. How much pie is there?

+ =

14

34+ =

There is of the pie left.

12

12

14

14

of the pie was left over after the party. Erick just ate of the pie. How much pie is left?

+ =

14

14=

12

12 - =

Subtracting fractions will help solve real-life problems.

2. Carmen bought of a pound of grapes and of a pound of nectarines.

How many pounds of fruit did Carmen buy?

3

42

8

_________________________________________________________

_

Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.

Add fractions. Hint: Add the numerators, keep the denominators the same.Reduce the sum, if possible.

Interpret the sum. “____ plus ____ equals _____.”


3

4a

What did you learn today about adding fractions with unlike denominators? (Pair-Share)Use words from the word bank.

Skill Closure

Access Common Core

Summary Closure


Which pair of fractions is ready to be added? Explain your answer.

3 34 7

A 3 14 4

B

3 1

4 8 1. 4: 4, 8, 12, 16

8: 8, 16, 24, 32

3

4

1

88

8

2

26

8

1

1

1

8

6 1

8 8

7

8

7

8

4: 4, 8, 12, 16 8: 8, 16, 32, 40

3

4

2

88

8

2

26

8

1

1

2

8

6 2

8 8

8

8

1Carmen bought pound of fruit

1

Word Bank

fractionslike/unlike

denominatorleast common denominatorequivalent

2. Carmen bought of a pound of grapes and of a pound of nectarines.

How many more pounds of nectarines than grapes did Carmen buy?

What did you learn today about subtracting fractions with unlike denominators? (Pair-Share) Use words from the word bank.

Access Common Core

Summary Closure

Read the problem and identify fractions, if necessary. (circle)Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.

Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.Reduce the difference, if possible.

Interpret the difference. “___ minus ____ equals ____.”


4

5a

To subtract fractions, both fractions must have like denominators.

Skill Closure

Which pair of fractions is ready to be subtracted? Explain your answer.

3 15 6

A 3 14 4

B

3 1

4 8 1. 4: 4, 8, 12, 16

8: 8, 16, 24, 32

3

4

1

88

8

2

2× ×

6

8

1

1

1

8

6 1

8 8

5

8

5

8

3

41

2

4: 4, 8, 12, 16 2: 2, 4, 6, 8

3

4

1

24

4

1

1× ×

3

4

2

2

2

4

3 2

4 4

1

41

4Carmen bought ____ of a pound more __________ than ___________.grapes nectarines

Word Bank

fractionslike/unlike

denominatorleast common denominatorequivalent

Independent Practice


6: 6, 12, 18, 24

1 2

6 3 1.

3: 3, 6, 9, 12

3 3

8 12 2.

3. The Smith family bought some pizzas. One pizza had left over. The other had left. How much pizza is there left over?

__________________________________________________________________

1

6

2

3

6

6

1

11

6

2

2

4

6

1 4

6 6

5

6

5

6

8: 8, 16, 24, 32 12: 12, 24, 36, 48

3

8

3

12

24

24

3

39

24

2

2

6

24

9 6

24 24

15

24

5

8

2

71

4

7: 7, 14, 21, 28, 35 4: 4, 8, 12, 16, 20, 24, 28

2

7

1

428

28

4

48

28

7

7

7

28

8 7

28 28

15

28

15

28There is of the pizza left over.

Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.

Add fractions. Hint: Add the numerators, keep the denominators the same.Reduce the sum, if possible.

Interpret the sum. “____ plus ____ equals _____.”


3

4a

Independent Practice

To subtract fractions, both fractions must have like denominators.

6: 6, 12, 18, 24

5 2

6 3 1.

3: 3, 6, 9, 12

3 3

8 12 2.

3. The Smith family bought a pizza. Jason ate of the pizza and Jamie ate of the pizza. How much more pizza did Jason eat than Jamie?

5

6

2

3

6

6

1

1×

×

5

6

2

2

4

6

5 4

6 6

1

6

1

6

8: 8, 16, 24, 32 12: 12, 24, 36, 48

3

8

3

12

24

24

3

3×

×

9

24

2

2

6

24

9 6

24 24

3

24

1

8

1

8

2

71

4

7: 7, 14, 21, 28, 35 4: 4, 8, 12, 16, 20, 24, 28

2

7

1

428

28

4

4× ×

8

28

7

7

7

28

8 7

28 28

1

28

1

28_________ ate ____ of a pizza more than _________.JamieJason

Read the problem and identify fractions, if necessary. (circle)Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.

Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.Reduce the difference, if possible.

Interpret the difference. “___ minus ____ equals ____.”


4

5a

Periodic Review 1

Access Common Core

7 1

12 4 1.

3 3

6 12 2.

3. Geoff has of a pound of cashews and buys of a pound of pecans. How many pounds of nuts does he have?

__________________________________________________________

3

41

6

Anita added the fractions below. Her teacher, Mrs. Caudill, says that her answer is incorrect. Explain the mistake that Anita made.

10 1

12 4

12: 12, 24, 36 4: 4, 8, 12, 16

7

12

1

4

12

12

1

17

12

3

3

3

12

7 3

12 12

10

12

5

6

5

6

6: 6, 12, 18, 24, 32 12: 12, 24, 36, 48

3

6

3

12

12

12

2

26

12

1

1

3

12

6 3

12 12

9

12

3

4

3

4

4: 4, 8, 12, 16 6: 6, 12, 18

3

4

1

612

12

3

39

12

2

2

2

12

9 2

12 12

11

12

11

12Geoff has of a pound of nuts

Anita did not make sure that the fractions had like denominators before adding. Instead, she just added both the numerators and denominators.

Periodic Review 1

Access Common Core

12: 12, 24, 36

11 1

12 4 1.

4: 4, 8, 12, 1611

12

1

4

12

12

1

1×

×

11

12

3

3

3

12

11 3

12 12

8

12

2

3

2

3

3 4

6 12 2.

6: 6, 12, 18, 24, 32 12: 12, 24, 36, 48

3

6

4

12

12

12

2

2×

×

6

12

1

1

4

12

6 4

12 12

2

12

1

6

1

6

3. Geoff has of a pound of cashews and buys of a pound of pecans. How many more pounds of cashews does he have than pecans?

Geoff has ____ of a pound more ___________ than __________.

3

41

6

4: 4, 8, 12, 16 6: 6, 12, 18

3

4

1

612

12

3

3× ×

9

12

2

2

2

12

9 2

12 12

7

12

7

12

Abdul subtracted the fractions below. His teacher, Mrs. Treadwell, says that his answer is incorrect. Explain the mistake that Abdul made.

10 1

12 4

pecanscashews

¼ was not converted to a common denominator first.

Also, denominators are incorrectly subtracted.

Periodic Review 2

Access Common Core

3 3

6 8 1.

3 1

10 4 2.

10: 10, 20, 30, 40 4: 4, 8, 12, 16, 20

3

10

1

4

20

20

2

2×

×

6

20

5

5

5

20

6 5

20 20

11

20

11

20

For each addition problem, place a check mark in the box to classify the sum as less than ½ or greater than ½.

6: 6, 12, 18, 24 8: 8, 16, 24

3

6

3

8

24

24

4

4×

×

12

24

3

3

9

24

12 9

24 24

21

24

7

8

7

8

3 1

6 8

1 1

3 9

3 1

4 12

1 4

6 5

1 1

4 5

less than ½ greater than ½.

Periodic Review 2

Access Common Core

6: 6, 12, 18, 24

4 3

6 8 1.

8: 8, 16, 24

9 1

10 4 2.

4

6

3

8

24

24

4

4×

×

16

24

3

3

9

24

16 9

24 24

7

24

7

24

10: 10, 20, 30, 40 4: 4, 8, 12, 16, 20

9

10

1

4

20

20

2

2×

×

18

20

5

5

5

20

18 5

20 20

13

20

13

20

Horatio added the fractions below. Some of his answers are incorrect. Circle all the incorrect answers and write the correct solutions.

Periodic Review 3

Access Common Core

7 1

12 4 1.

3 3

5 10 2.

12: 12, 24, 36 4: 4, 8, 12, 16

7

12

1

4

12

12

1

1×

×

7

12

3

3

3

12

7 3

12 12

10

12

5

6

5

6

5: 5, 10, 15, 2010: 10, 20, 30

3

5

3

10

10

10

2

2×

×

6

10

1

1

3

10

6 3

10 10

9

10

9

10

Choose Yes or No to show whether each choice

represents the sum of .

Yes No

Yes No

Yes No

Yes No

Periodic Review 3 (THIS PAGE IS HOMEWORK)

Access Common Core

12: 12, 24, 36

11 3

12 4 1.

4: 4, 8, 12, 16

3 3

5 10 2.

11

12

3

4

12

12

1

1×

×

11

12

3

3

9

12

11 9

12 12

2

12

1

6

1

6

5: 5, 10, 15, 2010: 10, 20, 30

3

5

3

10

10

10

2

2×

×

6

10

1

1

3

10

6 3

10 10

3

10

3

10

Choose Yes or No to show whether each choice is

equal to the difference of .

Yes No

Yes No

Yes No

Yes No

Documents

9 15