1. 5.3 Adding and Subtracting Unlike Fractions
LESSON
Adding and Subtracting Unlike Fractions
Hiking You are hiking between two campsites in the Chesapeake and Ohio Canal National Historic Park. The distance between the campsites is miles. You have already hiked miles. How many more miles do you have to hike? 10 1 5 3 4

2. 5.3
LESSON
Adding and Subtracting Unlike Fractions
To add or subtract fractions with different denominators, begin by using the LCD of the fractions to write equivalent fractions that have the same denominator.

3. 5.3 Adding and Subtracting Unlike Fractions 1
LESSON
Adding and Subtracting Unlike Fractions
EXAMPLE 1
Adding and Subtracting Fractions 5 12 1 3 + = 4 12 5 +
Write using LCD. 1 3
5 + 4 12 =
Write sum of numerators over denominator. 9 12 =
Add. 3 4 =
Simplify.

4. 5.3 Adding and Subtracting Unlike Fractions 1
LESSON
Adding and Subtracting Unlike Fractions
EXAMPLE 1
Adding and Subtracting Fractions 7 9 – 5 6 =
–15 18 14 –
Write fractions using LCD.
–15 – 14 18 =
Write difference of numerators over denominator.
–29 18 =
Subtract. 11 18 –1 =
Write fraction as a mixed number.

5. 5.3 Adding and Subtracting Unlike Fractions 2 Adding Mixed Numbers + =
LESSON
Adding and Subtracting Unlike Fractions
EXAMPLE 2
Adding Mixed Numbers + = 2 5 –4 6 11 –2
–22 5 +
–28 11
Write mixed numbers as improper fractions.
–242 55 = +
–140
Write fractions using LCD.
–242 + (–140) 55 =
Write sum of numerators over denominator.
–382 55 = 52 55 –6 =
Add. Then write fraction as a mixed number.

7. 5.3 Adding and Subtracting Unlike Fractions 3
LESSON
Adding and Subtracting Unlike Fractions
EXAMPLE 3
Subtracting Mixed Numbers
You are hiking between two campsites in the Chesapeake and Ohio Canal National Historic Park. The distance between the campsites is miles. You have already hiked miles. How many more miles do you have to hike? 10 1 5 3 4
SOLUTION
To find the remaining distance, subtract. – = 1 5 10 3 4 51 5 – 23 4
Write mixed numbers as improper fractions.
204 20 = –
115
Write fractions using LCD.
204 – 115 20 =
Write difference of numerators over denominator.

8. 5.3 Adding and Subtracting Unlike Fractions 3
LESSON
Adding and Subtracting Unlike Fractions
EXAMPLE 3
Subtracting Mixed Numbers
You are hiking between two campsites in the Chesapeake and Ohio Canal National Historic Park. The distance between the campsites is miles. You have already hiked miles. How many more miles do you have to hike? 10 1 5 3 4
SOLUTION
To find the remaining distance, subtract.
204 – 115 20 = 89 20 = = 9 20 4
Subtract. Then write fraction as a mixed number.
ANSWER
You need to hike miles, or about 4 miles. 9 20 1 2

10. 5.3 Adding and Subtracting Unlike Fractions 4
LESSON
Adding and Subtracting Unlike Fractions
EXAMPLE 4
Simplifying an Expression
Simplify the expression . a 2 6 – a 2 6 – = a 6 – 2 3 •
Write using LCD. a 2 a 6 – 3a =
Multiply. =
3a – a 6
Write difference of numerators over denominator. 2a 6 =
Subtract. 2a 6 = 1 3
Divide out common factor. a 3 =
Simplify.