A mixed fraction expresses the combination of an integer (whole number) and a fraction. For example, 3 2/3 is a mixed fraction. Squaring a number means multiplying it by itself; for example, 3^2 = 3*3 = 9.

Mixed fractions are often used in regular speech. For instance, if you asked a child how old he is, he might say “five and a half,” which would be written 5 1/2. He is unlikely to say “5.5,” “66 months” or “11 halves.”

Convert the Mixed Fraction to an Improper Fraction

Step 1

Find the denominator of the fractional part. For example, in the mixed fraction 5 2/3, 3 is the denominator.

Step 2

Multiply the integer portion by the denominator found in Step 1. In the example, 5*3 = 15.

Step 3

Find the numerator of the fractional part. In 5 2/3, 2 is the numerator.

Step 4

Add the result in Step 2 to the result in Step 3. In the example, 15 + 2 = 17.

Step 5

Write a fraction with the denominator from Step 1 and the result from Step 4 as numerator. In the example, you would write “17/3.”

Square the Fraction

Step 1

Square the numerator of the fraction in Section 1. In the example, 17*17 = 289.

Step 2

Square the denominator of the fraction in Section 1. In the example 3*3 = 9.

Step 3

Write a fraction with the numerator from Step 1 and the denominator from Step 2. In the example, you would write “289/9.”

Convert Back to a Mixed Fraction

Step 1

Divide the numerator of the fraction in Section 2 by its denominator, write the result as quotient and remainder. In the example, 289/9 = 32 with a remainder of 1.

Step 2

Write the whole number of the result in Step 1. In the example, you would write “32.” This is the numerator of the mixed fraction result.

Step 3

Write a fraction with the remainder from Step 1 as the numerator and the denominator from the fraction in Section 2 as the denominator. In the example, you would write “1/9.”

Step 4

Write the result of Step 2 and then Step 3. This is the mixed-fraction result, 32 1/9.