How to Convert between Improper Fractions and Mixed Numbers

By Angie Papple Johnston

The ASVAB Mathematics Knowledge subtest may throw some questions at you that will involve improper fractions and mixed numbers. You may even need to know how to convert an improper fraction to a mixed number—or vice versa.

If you have a fraction with a numerator larger than its denominator, you have an improper fraction. For example, 7/3 is an improper fraction. To put an improper fraction into simpler (proper) terms, you can change 7/3 into a mixed number (a number that includes a whole number and a fraction). Simply divide the numerator by the denominator: 7 divided by 3 gives you a quotient of 2 with a remainder of 1. There’s something left over because 3 doesn’t divide evenly into 7. The remainder becomes a numerator over the original denominator, so 1/3 is left over. Therefore, 7/3 is the same as

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If you want to multiply or divide a mixed number, you need to convert it into a fraction—an improper fraction. To make the change, convert the whole number into a fraction and add it to the fraction you already have. Here’s how:

1. Multiply the whole number by the denominator (bottom number) of the existing fraction to arrive at a new numerator.

Suppose you have

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Multiply 7 by 3: 7 × 3 = 21.

2. Place this new numerator over the existing denominator.

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3. Add that fraction to the original fraction to get the final answer.

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Or if you want to get technical, you can look at the whole process this way, too:

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Now, apply this technique to solve the following practice question.

Practice question

  1. A bin of hard candy holds

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How many 3/4-pound boxes of candy can be filled from the bin?

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Answer and explanation

  1. The correct answer choice is D.

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You can perform this operation by multiplying

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Divide 84 by 6, and the answer is 14.