Multiplying Improper Fractions and Proper Fractions
Use this worksheet to teach multiplying improper fractions and proper fractions. Work through one example with your student before assigning independent practice.
Teaching notes for parents and teachers
Use this worksheet to teach multiplying improper fractions and proper fractions. Work through one example with your student before assigning independent practice.
How to teach it
Use an area model to show a fraction of another fraction. Connect the overlap to multiplying numerators and denominators. Show how to convert mixed numbers before calculating and simplify using common factors.
Examples to explain together
Multiply 26 × 1 over 5 × 2, then simplify.
Multiply 98 × 2 over 11 × 3, then simplify.
If your student needs help
If your student cancels matching digits, distinguish digits from factors. If a mixed number is multiplied in separate parts incorrectly, model its equivalent improper fraction first.
Check understanding
Have your student estimate the product and explain its size. Division by a nonzero original factor should give the other factor.
Make a practice set
Select the worksheet, answer key, or both. When both are selected, the answer key prints after the questions. Keep it separate if you want your student to work independently.
After your student finishes
Review one problem together. Ask your student to explain the steps, then use the answer key to check the result. Revisit a difficult step before assigning another set.
About Multiplying Improper Fractions and Proper Fractions
Practice multiplying improper fractions and proper fractions. Focus on accuracy before speed. Use the space provided to record the steps you need.
How to practice
Write whole numbers over one and convert mixed numbers to improper fractions. Multiply the numerators and multiply the denominators. You may cancel common factors between a numerator and a denominator before multiplying, or simplify the product afterward. A common denominator is not required for multiplication.
Examples to explain together
Multiply 26 × 1 over 5 × 2, then simplify.
Multiply 98 × 2 over 11 × 3, then simplify.
If your student needs help
Do not multiply a mixed number’s whole part and fractional part separately and join them. Convert the entire mixed number first. Cancellation removes common factors, not digits that merely look alike.
Check understanding
Estimate the size of each factor. A positive factor below one reduces the other positive factor. Check by dividing by a nonzero original factor.
Before independent practice
Work through one example together. Ask the student to explain one step, then try a few questions independently. Review the cause of an error before repeating the calculation. Compare the student’s written steps with the answer key where worked steps are provided; a correct answer alone does not show which strategy was used.