Dividing Mixed Numbers by Improper Fractions
Use this worksheet to teach dividing mixed numbers by improper fractions. Work through one example with your student before assigning independent practice.
Teaching notes for parents and teachers
Use this worksheet to teach dividing mixed numbers by improper fractions. Work through one example with your student before assigning independent practice.
How to teach it
Start with a sharing or measurement model so the quotient has meaning. Then connect the model to multiplying by the divisor's reciprocal. Convert mixed numbers before applying the procedure.
Examples to explain together
Keep 26/5; multiply by the reciprocal 2/17, then simplify.
Keep 98/11; multiply by the reciprocal 3/29, then simplify.
If your student needs help
If your student flips the first fraction or both fractions, label the dividend and divisor. Use a simple example to check which reciprocal produces the correct quotient.
Check understanding
Ask your student to multiply the quotient by the original divisor. The product should equal the dividend.
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 Dividing Mixed Numbers by Improper Fractions
Practice dividing mixed numbers by improper fractions. Focus on accuracy before speed. Use the space provided to record the steps you need.
How to practice
Convert any mixed numbers to improper fractions and write whole numbers over one. Keep the first fraction, replace division with multiplication, and use the reciprocal of the second fraction. Multiply and simplify. The reciprocal is applied to the divisor only.
Examples to explain together
Keep 26/5; multiply by the reciprocal 2/17, then simplify.
Keep 98/11; multiply by the reciprocal 3/29, then simplify.
If your student needs help
Do not flip the first fraction or both fractions. Division by a fraction below one can produce an answer larger than the dividend; this is consistent with asking how many smaller groups fit.
Check understanding
Multiply the quotient by the original divisor, not its reciprocal. The result should equal the dividend.
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.