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Operations with Like and Unlike Fractions Study Guide

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Updated on Aug 24, 2011

Find practice problems and solutions for these concepts at Operations with Like and Unlike Fractions Practice Problems.

What's Around The Bend

  • Adding Like Fractions
  • Adding Unlike Fractions
  • Subtracting Like Fractions
  • Subtracting Unlike Fractions
  • Multiplying Fractions
  • Dividing Fractions
  • Reciprocals

In this chapter, we'll look at how to handle the four major operations—addition, subtraction, multiplication, and division—with like and unlike fractions.

Adding Like Fractions

Remember, like fractions are fractions that have the same denominator. To add two like fractions, add the numerators of the fractions. The denominator of your answer is the same as the denominator of the two fractions that you are adding.

Example

In this example, the two fractions are like fractions, because they both have a denominator of 5. The denominator of our answer will be 5. Add the numerators: 1 + 3 = 4. The numerator of our answer is 4.

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Example

The two fractions have a denominator of 12, so the denominator of our answer will be 12. Add the numerators: 6 + 4 = 10. The numerator of our answer is 10. . Because many tests ask for answers to be put in simplest form, let's reduce this fraction. The greatest common factor of 10 and 12 is 2.

= 5 and = 6.

+ .

Example

These fractions have a denominator of 9, so the denominator of our answer will be 9. Add the numerators: 1 + 2 + 3 = 6. The numerator of our answer is 6. . The greatest common factor of 6 and 9 is 3: = 2 and = 3.

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Inside Track

When adding two of the same fraction, keep the numerator of either fraction and divide the denominator of either fraction by 2. For example, . If the numerators of each addend are already in simplest form, then by adding this way, your answer will also be in simplest form. Let's check our answer: The greatest common factor of 6 and 10 is 2: = 3 and = 5; . = . If possible, reduce fractions before adding them. Be sure that after you reduce them, the fractions are still like fractions!

Adding Unlike Fractions

This title is a little misleading. We NEVER add unlike fractions. Instead, we find common denominators and convert the unlike fractions into like fractions. You already know how to add those! Remember, to find a common denominator for two unlike fractions, you must find the least common multiple of the two denominators.

Example

First, we must find a common denominator for these fractions. List a few multiples for each number:

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, …

8: 8, 16, 24, 32, 40, 48, 56, …

The least common multiple of 3 and 8 is 24. Convert each fraction to a number over 24: = 8, which means that the new denominator of the fraction is 8 times larger than the old denominator. Because we must always change the numerator in the same way that we change the denominator, multiply the old numerator by 8: 1 × 3 8 = 8. = . Now let's convert = 3, which means that the new denominator of is 3 times larger than the old denominator. Multiply the old numerator by 3: 2 × 3 = 6. . Now we have like fractions: . Add the numerators and keep the denominator: 8 + 6 = 14, so . Finally, let's simplify our answer. The greatest common factor of 14 and 24 is 2: = 7 and = 12.

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