Mixed Fraction Operations (Mixed Numbers)
16 problems on two pages that mix all four operations with mixed numbers, and many of the numbers are negative, like −3 7/10 − 1 1/5. Answers are in lowest terms, written as mixed numbers where needed. Use it as review in 7th grade, after fraction operations and the sign rules have both been taught.
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Settle the sign, then do the fractions
Each problem is two jobs. Work out the sign first. When multiplying or dividing, two negatives give a positive and one negative gives a negative. When adding or subtracting, picture a number line: −1 7/10 + 2 1/4 ends up just above zero, at 11/20.
Then convert every mixed number to an improper fraction before multiplying or dividing. 3 2/5 × 2 1/4 is 17/5 × 9/4, not 3 × 2 plus 2/5 × 1/4. Multiplying the whole numbers and the fractions separately is a common mistake, and it gives an answer that's too small.
Students who are shaky on the fraction steps should do mixed fraction operations with improper fractions first, which has no negatives. The guide to multiplying and dividing fractions walks through the steps.
Frequently Asked Questions
Do mixed numbers have to be converted to improper fractions?
For multiplying and dividing, yes. For adding and subtracting you can work with the whole numbers and fractions separately, but once negatives are involved, converting first is usually safer.
How do you divide two negative mixed numbers?
Convert both to improper fractions, flip the second one, and multiply. Two negatives make a positive. For (−3 4/7) ÷ (−3 5/7), that's 25/7 × 7/26, which is 25/26.
What grade is this sheet for?
7th grade, where operations with negative fractions are part of the rational number standards. Strong 6th graders can try it once they know the integer sign rules.