Answers to Fraction Problems: Solution Guide

Solutions to Fraction Problems

Equivalent Fractions

Two fractions are equivalent if the numerator (top number) and denominator (bottom number) of one fraction can be multiplied or divided by the same number to get the numerator and denominator of the other fraction. For example, 1/3 and 2/6 are equivalent fractions because one and three can both be multiplied by the same number (two) to get two and six (1 x 2 = 2 and 3 x 2 = 6). Likewise, you can reduce or simplify 2/6 to 1/3 by dividing two and six by two (2 ÷ 2 = 1 and 6 ÷ 2 = 3).

If you're adding or subtracting fractions with different denominators, like 6/7 and 5/6, you'll need to find equivalent fractions that have like denominators. The easiest way to do this is to multiply the numerator and denominator of each fraction by the other fraction's denominator, like this:

6/7 + 5/6

6/7 x 6/6 = 36/42

5/6 x 7/7 = 35/42

36/42 + 35/42 = 71/42

Comparing Fractions

If two fractions, like 1/4 and 3/4, have the same denominator, you can compare them by looking at their numerators. For instance, since three is greater than one, 3/4 is greater than 1/4.

If the fractions you're comparing have different denominators, you'll need to find equivalent fractions with a common denominator and compare the numerators of those fractions. For instance, to compare 2/6 and 3/4, write them as the equivalent fractions 4/12 and 9/12. Since nine is greater than four, 9/12 is greater than 4/12.

Adding and Subtracting Fractions

To add or subtract fractions with a common denominator, simply add or subtract their numerators. For instance, 6/7 - 5/7 = 1/7 because 6 - 5 = 1. If the fractions you're working with have different denominators, find equivalent fractions with a common denominator first, and then add or subtract those.

Multiplying Fractions

To multiply any two fractions together, even if they have different denominators, you simply multiply the numerators to get the numerator of the answer, and multiply the denominators to get the denominator of the answer. Then, simplify the solution, if necessary. Here are some examples:

3/5 x 1/8 = 3/40

1/4 x 4/4 = 4/16 = 1/4

5/3 x 8/7 = 40/21

Dividing Fractions

To divide two fractions, you'll multiply the dividend (fraction being divided) by the reciprocal of the divisor (fraction you're dividing by). To find a fraction's reciprocal, just reverse the numerator and the denominator. For instance, the reciprocal of 2/9 is 9/2. To divide 1/2 by 2/9, multiply 1/2 and 9/2 to get 9/4 (1/2 x 9/2 = 9/4).