Mixed Fraction Operations (Improper)
20 fraction problems on two pages that mix adding, subtracting, multiplying, and dividing. The fractions are all positive, some of them improper, and the answer key leaves answers as improper fractions in lowest terms, like 81/35. Use it as review in 6th grade, after all four fraction operations have been taught.
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Different rules for different signs
The hard part of a mixed sheet is switching rules from one problem to the next. Adding and subtracting need a common denominator. Multiplying goes straight across. Dividing means flipping the second fraction and multiplying. Have students circle the sign before they start each problem.
Finding a common denominator before multiplying isn't wrong, just slow. The real mistake goes the other way: adding straight across, so 1/5 + 3/2 turns into 4/7. The right answer is 17/10.
Simplify at the end and leave the answer as an improper fraction to match the key. For the same kind of problems with mixed numbers and negatives, move on to mixed fraction operations with mixed numbers.
Frequently Asked Questions
Should the answers be written as mixed numbers?
The answer key leaves them as improper fractions in lowest terms, like 81/35. Many teachers accept either form, but converting to a mixed number is an extra step this sheet doesn't ask for.
Why do you flip the second fraction when dividing?
Dividing by a fraction is the same as multiplying by its reciprocal. Dividing by 3/2 asks how many 3/2s fit, and multiplying by 2/3 gives the same answer. So 1/3 ÷ 3/2 = 1/3 × 2/3 = 2/9.
What grade covers all four fraction operations?
5th grade adds, subtracts, and multiplies fractions, and 6th grade adds dividing a fraction by a fraction. This sheet fits 6th grade and later review.