Mixed Numbers and Improper Fractions Worksheets

Pass out the page and tell students to check the direction of each problem before they start. Twenty problems usually take fifteen minutes. For improper to mixed, they divide the top by the bottom; for mixed to improper, they multiply the whole number by the denominator and add the top. Write both rules on the board. Use the key to check, then ask a student to explain one of each type. Five versions make a good quiz series.

A mixed number and an improper fraction are two ways of writing the same amount. Children need division facts for one direction and multiplication facts for the other. Alternating the two keeps students from following one procedure on autopilot, and tests do the same. The fraction part is already in lowest terms, so nothing needs reducing here. Common slips are forgetting to add the numerator back, or writing the remainder over the wrong number.

Up to 6 limits the denominators and the whole parts, which suits a first sitting. Up to 10 and Up to 12 mean larger whole parts and trickier division. Twelve problems per page suits students who need to talk through each step. Try drawing models for one of each type. Missing number mode works as an extension for students who want a reasoning problem.

Why mix both directions on one page?

Each direction is easy alone and confusing together, and tests mix them. A student who can tell which conversion a problem needs has understood what a mixed number is.

How are the answers written?

Improper to mixed: whole number then fraction, as in 2 3/4. Mixed to improper: a single fraction, as in 16/5. The fraction part never needs reducing on this page.

What is the quickest way to convert a mixed number?

Multiply the whole number by the denominator, add the numerator, and keep the denominator. For 3 1/5 that is 3 times 5, plus 1, giving 16/5. Reverse by dividing 16 by 5 to get 3 remainder 1.