Mixed operations
Four operation vertical practice
Practice six problems per operation in one document, with independent digit widths, regrouping settings and long-division remainder options.
Preview and downloadMixed operations practice
Mixed operations with fractions
Solve twelve proper-fraction problems, three per operation, with exact reduced answers and worked keys. Choose grouped or randomized operation order.
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Read the operator first. Use a common denominator for addition or subtraction, multiply for products, and multiply by the reciprocal for division.
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Choose the operations and the amount of support
Choose by the learner’s current skills. Mixing operations adds the task of recognizing a sign before choosing a method, even when the individual numbers are familiar.
The preview shows the first student page. Downloads contain the complete worksheet; the version with answers adds a separate key with matching problem positions. More spacious written-method practice may use several pages.
Learning objective
What this activity builds
Switch correctly between denominator-based addition and subtraction, multiplication, and reciprocal division.
Worked example
2/3 ÷ 1/4 = ?
8/3 = 2 2/3
Multiply 2/3 by the reciprocal 4/1 to get 8/3. The improper result is two wholes and two thirds.
Teaching notes
Make the practice count
- The printed operands are positive proper fractions drawn from the selected numerator and denominator pools. Answers can be improper.
- Ordered practice uses three additions, then three subtractions, three multiplications and three divisions; randomized practice mixes their positions.
- Subtraction answers are nonnegative. Keys show valid calculation steps and reduced answers, including mixed numbers when appropriate.
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Read equal-area fraction circles from selected denominator groups. Optionally label each equal part; reference cards identify the total shaded fraction.
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