6th Grade Math Textbook, Fundamentals

 &KDSWHU

5-6

Remember:

 ab ba ab

Add with Unlike Denominators, Like Signs

Add: ()

• Find the LCD of the fractions.
  Multiples of 7: 7, 14, 21...
  Multiples of 14: 14, 28...
  The LCD is 14.


• Use the LCD to rename one or both
  fractions.

 

• Add. Express the sum in lowest terms.

() 1

So ()1.

The addends are both negative,

so the sum is negative.

1

14

 9

14

3

7

1

14

15

14

 6 ( 9 )

14

 9

14

6

14

6

14

3

7

3 • 2

7 • 2

 9

14

3

7

Add with Unlike Denominators, Unlike Signs

Add: ()

• Find the LCD of the fractions.
  Multiples of 6: 6, 12, 18, 24...
  Multiples of 9: 9, 18, 27...
  The LCD is 18.


• Use the LCD to rename one or both
  fractions.



 

• Add. Express the sum in lowest terms.

( )

So^56 () 92 ^1118.

The positive addend has the greater

absolute value, so the sum is positive.

4

18

15

18

11

18

15 ( 4 )

18

4

18

2 •2

9 • 2

 2

9

15

18

5 •3

6 • 3

5

6

 2

9

5

6

Update your skills. See page 414 XVI.

Add and Subtract Fractions

Objective To add and subtract positive and negative fractions

In this year’s car race, the second-place car reached the

finish line second behind the winner. The third-place car

reached the finish line second after the second-place car.

How many seconds behind the winner was the third-place car?

To find the number of seconds, add .

• The fractions have unlike denominators, so find the
  LCD of and.
  Multiples of 2: 2, 4, 6, 8...
  Multiples of 8: 8, 16, 24...
  The LCD of 2 and 8 is 8.


• Rename one or both fractions using the LCD.



• Add. Express the sum in lowest terms.

 1 Write in simplest form.

So the third-place car finished 1 seconds behind the winner.

To add fractions with like or unlike signs, apply the same sign rules

you use for adding integers. If the fractions have unlike denominators,

use the LCD to find a common denominator.

5

8

1

2

1

8

1

8

5

8

4

8

9

8

4  5

8

1 • 4

2 • 4

4

8

1

2

5

8

1

2

5

8

1

2

A fraction greater than 1 is in simplest

form, or lowest terms, when it is a

mixed number and 1 is the only

common factor of the numerator and

denominator of its fraction part.