By now in this chapter, you have practiced multiplying, dividing, adding, and subtracting fractions. The following table summarizes these four fraction operations. Remember: You need a common denominator to add or subtract fractions, but not to multiply or divide fractions
Summary of fraction operations
Fraction multiplication: Multiply the numerators and multiply the denominators.
Fraction division: Multiply the first fraction by the reciprocal of the second.
Fraction addition: Add the numerators and place the sum over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD.
Fraction subtraction: Subtract the numerators and place the difference over the common denominator. If the fractions have different denominators, first convert them to equivalent forms with the LCD.
Simplify:
ⓐ
ⓑ
Solution
First we ask ourselves, “What is the operation?”
ⓐ The operation is addition.
Do the fractions have a common denominator? No.
Find the LCD.
Rewrite each fraction as an equivalent fraction with the LCD.
Simplify the numerators and denominators.
Add the numerators and place the sum over the common denominator.
Check to see if the answer can be simplified. It cannot.
ⓑ The operation is division. We do not need a common denominator.
To divide fractions, multiply the first fraction by the reciprocal of the second.
Use the order of operations to simplify complex fractions
In
Multiply and Divide Mixed Numbers and Complex Fractions , we saw that a complex fraction is a fraction in which the numerator or denominator contains a fraction. We simplified complex fractions by rewriting them as division problems. For example,
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