Adding and Subtracting Like Fractions
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.
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.
