How To Estimate Sum & Differences With Fractions

Estimation is an important skill in math and in everyday life. Adding and subtracting fractions can be complicated because they are not whole numbers; they represent a portion of a whole. Knowing how to estimate the sum or difference of two fractions can save you a lot of work and at the same time provide an approximate answer.

Step 1

Know the rules of rounding a fraction to the nearest 1/2. According to these rules, the fraction will be rounded to 0, 1/2 or 1. A fraction whose value is less than 1/4 will be rounded down to 0, a fraction greater than or equal to 1/4 and less than or equal to 3/4 will be rounded to 1/2 and a fraction greater than 3/4 will be rounded to up 1. For example, 4/16 rounds to 1/2, 3/16 rounds to 0 and 13/16 rounds up to 1.

Step 2

Convert the fractions and then add or subtract. If the math problem is 9/16 + 5/12, by rounding the fractions to the nearest 1/2, your new math problem becomes 1/2 + 1/2, which equals 1. The fraction 9/16 rounds to 1/2 because it is less than 12/16 (3/4) and greater than 4/16 (1/4). The fraction 5/12 rounds to 1/2 because it is less than 9/12 (3/4) but greater than 3/12 (1/4). When subtracting the fractions, 1/2 (9/16) – 1/2 (5/12) = 0

Step 3

Solve the full problem to show how close you were to the exact answer. If the problem was done without estimating, you would convert 9/16 to 27/48 and 5/12 to 20/48 so that the fractions have the same denominator. Then 27/48 + 20/48 = 47/48. The fraction 47/48, which is equivalent to 0.979, is close to 1. Subtraction is done the same way. 27/48 – 20/48 = 7/48 (0.145). The result is close to 0.