6th Grade Math Textbook, Fundamentals

Update your skills. See page 414 XVI.

Addition and Subtraction Equations

with Fractions

Objective To apply the Subtraction Property of Equality to solve addition equations with

fractions • To apply the Addition Property of Equality to solve subtraction equations with fractions

Herman packages nails for a hardware company. He weighs
them instead of counting the individual nails. If the scale already

shows pound, what fraction of a pound of nails does he need

to make a -pound package?

To find the amount, write an addition equation, and apply the

Subtraction Property of Equality.

Let xthe fraction of a pound of nails needed.

Solve:x

x   

x 

x Express in simplest form.

Check:x

 Substitute for x.

 Rename as fractions with a common denominator, then add.

 Tr u e

So Herman needs pound of nails to make a -pound package.

To solve an addition equation with signed fractions, follow the

same rules as you use to add and subtract integers.

Solve:n()

n()() ()

n 

n

n

n

Simplify. Divide the numerator

and denominator by their GCF, 3.

Use the Subtraction Principle.

Add.

3

8

3

16

3

16

9

16

3

8

3

5

9  3

15  3

9

15

3

15

6

15

 6

15

 6

15

3

15

 6

15

 6

15

3

15

3

16

9

16

9

16

9

16

3

16

6

16

?^9

16

?^9

16

3

8

9

16

3

16

9

16

6

16 Rename as fractions with a common

denominator, then subtract.

3

8

3

8

9

16

3

8

3

8

9

16

 &KDSWHU

5-14

Remember:

Subtraction Property of Equality

If a b, then a c b c.

Subtract from both sides

to isolate x.

3

8

Subtract from both

sides to isolate n.

 6

15

Check:n()

()

()

153  153 Tr u e

3

15

 (^6) ?
15
9
15
3
15
 (^6) ?
15
3
5
3
15
 6
15