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© Edgenuity, Inc. 1 Warm-Up Adding and Subtracting Fractions Lesson Goals Solve real-world addition and subtraction problems involving fractions. Use a number line to add and subtract signed fractions. and differences of fractions. Estimate Use fraction to add and subtract signed fractions. Lesson Question Words to Know Fill in this table as you work through the lesson. You may also use the glossary to help you. the result of adding two or more numbers the opposite of a number (verb) to form an approximate opinion of worth, amount, size or weight; (noun) an approximate calculation fractions that have the same numerical value W K 2 ?

Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

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Page 1: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 1

Warm-Up Adding and Subtracting Fractions

Lesson Goals

Solve real-world addition and subtraction problemsinvolving fractions.

Use a number line to addand subtract signedfractions.

and di�erences offractions.

EstimateUse fraction

to add and subtract signedfractions.

Lesson Question

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

the result of adding two or more numbers

the opposite of a number

(verb) to form an approximate opinion of worth, amount, size or weight; (noun) an approximate calculation

fractions that have the same numerical value

WK2

?

Page 2: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 2

Instruction Adding and Subtracting Fractions

2Slide

Subtracting Fractions

Use fraction bars to model subtracting fractions.

Problem: − −5

6

1

2

Find a common denominator.

Our common denominator will be , because 6 is the lowest common multiple of 2 and 6.

Rewrite the problem using the common denominator.

= + −

= − = − =

− −

5

65

6

3

6

8

612

6

= + −

= − = − =

− −

5

65

6

3

6

8

612

6

= + −

= − = − =

− −

5

65

6

3

6

8

612

6

Drag the fraction bars to the number line.

−126

−56

−36

−1 0 1

2 3 4 5 6 8 10 12

= + −

= − = − =

− −

5

65

6

3

6

8

612

6

= + −

= − = − =

− −

5

65

6

3

6

8

612

6

Page 3: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 3

Instruction Adding and Subtracting Fractions

3Slide

Adding Fractions

Problem: − − −

2

5

1

2

Use the additive inverse to rewrite the problem.

− +

2

5

1

2

The lowest common denominator is 10.

− +4

10

Drag the fraction bars to the dots on the number line.

− =5

10

4

10

−1 0 1110

− 410+ 5

10

2 3 4 5 6 8 10 12

− +4

10

− =5

10

4

10

Page 4: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 4

Instruction Adding and Subtracting Fractions

Adding and Subtracting Fractions on a Number Line

Find the sum p + q, where both p and q are fractions.

Locate p on thenumber line.

If q is positive…

If q is negative…the left.

Move spaces to q

qMove spaces to

the .

To find p − q, change to addition with the of q, or p + (− q).

Using a Number Line to Add Fractions

Find the using equivalent fractions.

− + = − + =11

2

3

4

3

2

3

4 − + − = − + − =

11

2

3

4

3

2

3

4

−2 −1 0−52 −94 −74 −32 −54 −34 −12 −14

− + = − + =11

2

3

4

3

2

3

4− + − = − + − =

11

2

3

4

3

2

3

4

2Slide

Page 5: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 5

Instruction Adding and Subtracting Fractions

Using a Number Line to Subtract Fractions

Find the by using the additive inverse.

−− = = + − = + − =

3

5

3

511

2

3

5

3

2

6

10

15

10 −− = = + − = + − =

3

5

3

511

2

3

5

3

2

6

10

15

10

0− 910

610

−− = = + − = + − =

3

5

3

511

2

3

5

3

2

6

10

15

10−− = = + − = + − =

3

5

3

511

2

3

5

3

2

6

10

15

10

2Slide

Subtracting Fractions

− − = =21

213

421

213

4

2 3

1

4214 212 23

4 314

14

14

14

312 41

4 41233

4

4

− − = =21

213

421

213

4

Page 6: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 6

Instruction Adding and Subtracting Fractions

7Slide

Estimating with Compatible Fractions

Marci’s Cocoa Surprise recipe calls for several ingredients, all of which are listed in fractions. Marci wants to know if the ingredients will fit in a 3-cup bowl.

The ingredients include: 3

7 cup sugar,

2

5 cup cocoa,

1

2 cup flour, and

5

8 cup milk.

What is the approximate sum of these measures?

≈3

7

1

2

2

5≈2

5≈

≈5

8

1

2

Based on the approximations, Marcy’s ingredients will fit in her 3- bowl.

Sum of these measures

+ + +1

2

1

2

1

2

1

2

cups

Page 7: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 7

Instruction Adding and Subtracting Fractions

9Slide

Checking a Solution

Joaquim jogged 56

mile from his home on a straight road. Then he turned around

and ran 21

8 miles in the opposite direction. How far is Joaquim from home?

−5

621

8

A common denominator for 6 and 8 is .

−= 51

24 −= 51

24

= − 3124

We know that distance is a positive value, so we’ll take the absolute value.

Joachim ran 17

24from home.

We can now check our answer using estimation.

1 − 2 = −1 =

≈17

241

Our answer is reasonable.

−= 51

24

Since we’re taking the

absolute value

Page 8: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 8

Summary Adding and Subtracting Fractions

? Lesson Question How do you add and subtract positive and negative fractions?

Answer

Review: Key Concepts

Adding and Subtracting Fractions

• Find a Denominator

• Adding Fractions

• Same signs: Add the absolute values. The sum has the sign as the addends.

• Different signs: Find the difference of the values. The

sum has the same sign as the addend with the greater absolute value.

Subtracting Fractions

• Add the .

2

Page 9: Warm-Up Adding and Subtracting Fractions€¦ · Instruction Adding and Subtracting Fractions Adding and Subtracting Fractions on a Number Line Find the sum p + q, where both p and

© Edgenuity, Inc. 9

Summary Adding and Subtracting Fractions

Use this space to write any questions or thoughts about this lesson.