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PRE-ALGEBRA
Lesson 5-3 Warm-Up
PRE-ALGEBRA
Adding and Subtracting
Fractions (5-3)
How do you add
fractions with
unlike
denominators?
To add fractions with unlike denominators (different-sized parts), change the
fractions to equivalent fractions with the same denominators (same-sized
parts). Then, add the numerators (number of parts). The denominators stay the
same.
 Write equivalent fractions with 
a common denominator (notice
each fraction is multiplied by the
other fraction’s denominator)

Add the numerators.

PRE-ALGEBRA
Adding and Subtracting
Fractions (5-3)
How do you
subtract fractions
with unlike
denominators?
Subtracting fractions is similar to adding fractions. If the fractions have unlike
denominators (different-sized parts), change the fractions to equivalent
fractions with the same denominators (same-sized parts). Then, you can
subtract the numerators (number of parts).
Example:
 Write equivalent fractions with a common
denominator. Note that you can do this by
multiplying each fraction by the other
fractions denominator.
 Subtract the numerators.
PRE-ALGEBRA
Adding and Subtracting Fractions
LESSON 5-3
Additional Examples
Find each sum or difference. Simplify if possible.
a. 4 + 2
9
9
4 2
4+2
+ =
9 9
9
6
9
2
=
3
=
12
Add the numerators.
Simplify.
Simplify.
5
b. b – b
12 – 5
12
5
–
=
b
b
b
7
= b
Subtract the numerators.
Simplify.
PRE-ALGEBRA
Adding and Subtracting Fractions
LESSON 5-3
Additional Examples
Simplify each difference.
a.
1 3
–
6 4
1 3 (1 • 4) – (3 • 6)
– =
6 4
6•4
4 – 18
=
24
= –14
24
= –7
12
Use a common denominator.
Simplify.
Simplify.
Simplify.
2
5
b. y – 16
2
– 5 = (2 • 16) – (5 • y) Use a common denominator.
y
16
y • 16
= 32 – 5y
Simplify.
16y
PRE-ALGEBRA
Adding and Subtracting Fractions
LESSON 5-3
Additional Examples
5
4
Find 6 + 15 .
5
5
4
+ 4 =
+
6 15
2•3 3•5
=
5•5
+ 4•2
2•3•5 3•5•2
25 8
+
30 30
33
=
30
=
11
10
= 11
10
=
Write the prime factorizations of the
denominators.
Rewrite the fractions using the LCD, 2 • 3 • 5.
Simplify.
Add the numerators.
Simplify.
Write the fraction as a mixed number.
PRE-ALGEBRA
Adding and Subtracting Fractions
LESSON 5-3
Additional Examples
1
One day you rode a bicycle for 3 hours, and
2
1
jogged for 1 hours. How many hours did you exercise?
4
1
1
7
5
3 +1 = +
2
4
2
4
7
5
= + 2
2
2
Write mixed numbers as improper fractions.
Write the prime factorizations of the
denominators.
Rewrite the fractions using the LCD, 22.
7•2
+ 52
2•2
2
14
= + 5
4
4
= 19
4
= 43
4
=
Simplify.
Add the numerators.
Write the fraction as a mixed number.
3
You exercised for 4 4 hours.
PRE-ALGEBRA
Adding and Subtracting Fractions
LESSON 5-3
Lesson Quiz
Find each sum or difference.
2
10
1. 24 + 24
1
2
3
1
2. 5 4 – 2 8
5
38
3. – 3 – 1
5
– 14
15
3
4. 4 + 3
7
2c
8c + 21
14c
PRE-ALGEBRA