Fractions
Cross-cancel before multiplying fractions
Reduce common numerator and denominator factors before multiplication to keep the product calculation manageable.
Preview and downloadFractions practice
Dividing fractions
Create a dividing fractions worksheet with 10 or 15 proper-fraction problems, three difficulty ranges, exact reduced answers, and a separate answer key.
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Keep the first fraction unchanged. Replace division by multiplication using the reciprocal of the second fraction, then simplify. Multiply the quotient by the original divisor to check the result.
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Customize this worksheetLearning objective
What this activity builds
Distinguish dividend and divisor, use the reciprocal of the divisor and verify the quotient by multiplication.
Worked example
Find 3/4 ÷ 2/5.
(3/4) × (5/2) = 15/8 = 1 7/8.
The divisor is 2/5, whose reciprocal is 5/2. The quotient describes how many two-fifths-sized groups fit into three-fourths, including a fractional group. Multiplying 15/8 by 2/5 returns 3/4.
Teaching notes
Make the practice count
- Name the dividend and divisor before changing the operation.
- Use a strip model to show why division by a proper fraction can increase the numerical result.
- Keep the original problem available for the multiplication check.
Choose a dividing fractions worksheet
Start with the default Friendly numbers for denominators 2, 3, 4, 5 and 10. Move to denominators 2 through 10 or 2 through 20 when learners are ready for a wider range, then choose 10 or 15 problems for the amount of practice needed.
Every problem divides one positive proper fraction by another. Learners keep the dividend, multiply by the reciprocal of the nonzero divisor and reduce the exact quotient; the answer key shows those reciprocal and multiplication steps.
What changes between the three difficulty choices?
Friendly numbers uses denominators 2, 3, 4, 5 and 10 with numerators through 9. The next level uses denominators 2 through 10 and numerators through 9; the highest uses denominators 2 through 20 and numerators through 19.
How can I check a fraction quotient?
Multiply the reduced quotient by the original divisor. If the division is correct, that product equals the original dividend.
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