5.2
Adding and Subtracting
Like Fractions
Goal: Add and subtract like fractions.
Adding and Subtracting Like Fractions
Words To add or subtract fractions with the same denominator,
write the sum or difference of the numerators over the denominator.
4
9
1
9
9
2
!! # !! " !!
11
11
11
Numbers !! ! !! " !!
a
c
9
b
c
Algebra !! ! !! " !!, c $ 0
Example 1
c
a
b
!! # !! " !!, c $ 0
c
c
c
Adding Like Fractions
A survey asked 100 students
ages 7 to 11 what sports
apparel they prefer to wear.
The circle graph at the right
summarizes their responses.
What fraction of the students
responded either major league
baseball or NBA?
Other
9
Apparel Survey
NFL
30
Pro wrestling
17
NBA
21
Major league
baseball
23
Solution
To find the fraction of the students who responded either major
league baseball or NBA, find the sum of
!
.
Write sum of numerators
over denominator.
"
"
and
"
Add. Then simplify.
Answer: The fraction of the students who prefer either major
league baseball or NBA apparel is
90
Chapter 5 • Pre-Algebra Notetaking Guide
.
Copyright © Holt McDougal. All rights reserved.
5.2
Adding and Subtracting
Like Fractions
Goal: Add and subtract like fractions.
Adding and Subtracting Like Fractions
Words To add or subtract fractions with the same denominator,
write the sum or difference of the numerators over the denominator.
4
9
1
9
5
7
9
2
!! # !! " !!
11
11
11
Numbers !! ! !! " !!
a
c
b
c
9
a#b
Algebra !! ! !! " !!, c $ 0
Example 1
c
a"b
a
b
!! # !! " !!, c $ 0
c
c
c
Adding Like Fractions
A survey asked 100 students
ages 7 to 11 what sports
apparel they prefer to wear.
The circle graph at the right
summarizes their responses.
What fraction of the students
responded either major league
baseball or NBA?
Other
9
Apparel Survey
NFL
30
Pro wrestling
17
NBA
21
Major league
baseball
23
Solution
To find the fraction of the students who responded either major
23
21
! and !! .
league baseball or NBA, find the sum of !
100
100
23
21
!! ! !!
100
100
23 # 21
!
" !
100
Write sum of numerators
over denominator.
11
44
! " !!
" !
25
100
Add. Then simplify.
Answer: The fraction of the students who prefer either major
11
league baseball or NBA apparel is !25! .
90
Chapter 5 • Pre-Algebra Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Subtracting Like Fractions
Example 2
When you perform
operations with
negative fractions, be
sure to assign a
negative sign in front
of a fraction to the
numerator of the
fraction.
4
9
Write difference of numerators
over denominator.
3
9
a. !!! ! !! "
Subtract.
"
!
2
11
4
11
"
b. !! ! !!! "
4
11
To subtract !!!, add
#
"
Write sum of numerators
over denominator.
"
Add.
.
Checkpoint Find the sum or difference.
2
7
4
7
3
13
1. !! # !!
Adding and Subtracting Mixed Numbers
Example 3
3
7
6
7
a. 4 !! # 3 !! "
Write mixed numbers as
improper fractions.
#
Write sum of numerators
over denominator.
"
"
3
10
Add. Then write fraction
as mixed number.
"
9
10
b. 11!! ! 8 !! "
!
"
Write mixed numbers as
improper fractions.
Write difference of numerators
over denominator.
"
Copyright © Holt McDougal. All rights reserved.
8
13
2. !! ! !!
"
Subtract. Then write fraction
as mixed number.
Chapter 5 • Pre-Algebra Notetaking Guide
91
Subtracting Like Fractions
Example 2
When you perform
operations with
negative fractions, be
sure to assign a
negative sign in front
of a fraction to the
numerator of the
fraction.
4
9
Write difference of numerators
over denominator.
3
9
#4 # 3
a. !!! ! !! " !9!
7
Subtract.
" #!9!
!
2
4
"
2
4
# !1!
b. !! ! !!! " !1!
1
1
11
11
4
11
4
To subtract !!!, add !1!
.
1
2"4
" !1!
1
Write sum of numerators
over denominator.
6
" !1!
1
Add.
Checkpoint Find the sum or difference.
2
7
4
7
3
13
1. !! # !!
6
!!
7
5
13
!!!
Adding and Subtracting Mixed Numbers
Example 3
3
6
31
27
a. 4 !! # 3 !! " !7! # !7!
7
3
10
7
Write mixed numbers as
improper fractions.
31 " 27
" !7!
Write sum of numerators
over denominator.
58
2
" !7! " 8 !7!
Add. Then write fraction
as mixed number.
9
10
113
!
b. 11!! ! 8 !! " !
10
Copyright © Holt McDougal. All rights reserved.
8
13
2. !! ! !!
89
! !10!
Write mixed numbers as
improper fractions.
113 ! 89
!
" !
10
Write difference of numerators
over denominator.
24
2
" !10! " 2 !5!
Subtract. Then write fraction
as mixed number.
Chapter 5 • Pre-Algebra Notetaking Guide
91
Simplifying Variable Expressions
Example 4
4a
21
Write sum of numerators
over denominator.
10a
21
a. !! ! !! "
"
Add.
"
Simplify.
!
9
5b
4
5b
"
b. #!! # #!! "
!
4
5b
To subtract #!! , add
"
Write sum of numerators
over denominator.
"
Add.
"
Simplify.
.
Checkpoint Find the sum or difference.
2
11
4
11
3. 3 !! ! 5 !!
2a
25
8a
25
5. !! ! !!
92
Chapter 5 • Pre-Algebra Notetaking Guide
5
13
6
13
4. #4 !! # 3 !!
17
3c
!
5
3c
"
6. #!! # #!!
Copyright © Holt McDougal. All rights reserved.
Simplifying Variable Expressions
Example 4
4a
10a
4a # 10a
!
a. !! ! !! " !21
21
21
Write sum of numerators
over denominator.
14a
" !2!
1
Add.
" !2a!
Simplify.
3
!
"
9
9
4
4
b. #!! # #!! " "!5b! ! !5b!
5b
5b
4
4
To subtract #!! , add !5b! .
5b
"9 # 4
" !5b!
Write sum of numerators
over denominator.
"5
" !
!
Add.
5b
1
" "!b!
Simplify.
Checkpoint Find the sum or difference.
2
11
4
11
5
13
3. 3 !! ! 5 !!
6
13
4. #4 !! # 3 !!
11
13
6
11
8 !!
2a
25
8a
25
17
3c
5. !! ! !!
Chapter 5 • Pre-Algebra Notetaking Guide
!
5
3c
"
6. #!! # #!!
2a
!!
5
92
#7!!
4
c
"!!
Copyright © Holt McDougal. All rights reserved.