Practice Mixed-Improper Conversion in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The process of converting between mixed-number form and improper-fraction form, which represent the same value.

Mixed to improper: multiply the whole number by the denominator, add the numerator, keep the denominator. Improper to mixed: divide numerator by denominator to get the whole part and remainder.

Showing a random 20 of 50 problems.

Example 1

medium
Convert 1008\dfrac{100}{8} to a mixed number and simplify.

Example 2

medium
Convert 193\frac{19}{3} to a mixed number.

Example 3

hard
Express 2009\dfrac{200}{9} as a mixed number.

Example 4

hard
Find a whole number nn so that n37=457n\frac{3}{7} = \dfrac{45}{7}.

Example 5

easy
A ribbon is 94\dfrac{9}{4} meters long. Write it as a mixed number.

Example 6

easy
Convert 3273\frac{2}{7} to an improper fraction.

Example 7

hard
Find the value: 312×473\frac{1}{2} \times \dfrac{4}{7}.

Example 8

medium
Convert 5385\frac{3}{8} to an improper fraction, then state the numerator.

Example 9

challenge
Find a whole number nn so that n25=325n\frac{2}{5}=\frac{32}{5}.

Example 10

medium
Without dividing, explain why 507\dfrac{50}{7} is between 77 and 88, then give its mixed form.

Example 11

challenge
For what positive integers nn does n6\dfrac{n}{6} equal a mixed number with whole part exactly 44?

Example 12

medium
Convert 7210\dfrac{72}{10} to a mixed number and simplify the fraction part.

Example 13

medium
A board is 174\frac{17}{4} feet long. Write its length as a mixed number.

Example 14

easy
Convert 7127\frac{1}{2} to an improper fraction.

Example 15

easy
Convert 254\dfrac{25}{4} to a mixed number.

Example 16

easy
Convert 92\frac{9}{2} to a mixed number.

Example 17

medium
Convert 478\dfrac{47}{8} to a mixed number.

Example 18

medium
Convert 456\frac{45}{6} to a mixed number and simplify the fraction part.

Example 19

medium
Convert 307\frac{30}{7} to a mixed number.

Example 20

easy
Convert 4124\frac{1}{2} to an improper fraction.
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