Divide Fractions Using an Inverse Multiplication
Rewrite the division as multiplication by the divisor’s reciprocal.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For (5/6)÷(2/3), use (5/6)(3/2)=15/12=5/4.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A fraction quotient asks how many divisor-sized amounts fit in a dividend. Multiplication by the divisor’s reciprocal solves that relationship because divisor times reciprocal is one. The quotient can exceed one even when both inputs are fractions. Interpret a fractional quotient rather than silently reporting only complete pieces.
Rewrite the division as multiplication by the divisor’s reciprocal. Multiply and simplify, then check quotient × original divisor = dividend. Explain whether the prompt requests the full mathematical quotient or only complete pieces.
Take the reciprocal of the divisor, not the dividend. A full fractional quotient and a count of complete pieces are different requests. Write divisor × unknown = dividend before applying reciprocal multiplication.
- Write divisor × unknown = dividend before applying reciprocal multiplication.
- Work through the supplied example and label what each number or attribute represents.
- Rewrite the division as multiplication by the divisor’s reciprocal.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
For (5/6)÷(2/3), use (5/6)(3/2)=15/12=5/4. Check (5/4)(2/3)=5/6. The full quotient is 1 1/4 divisor-sized amounts. Only one complete such amount fits, but the quotient also counts the quarter of another. Take the reciprocal of the divisor, not the dividend. A full fractional quotient and a count of complete pieces are different requests. Write divisor × unknown = dividend before applying reciprocal multiplication.
Check your reasoning
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Helpful tips
- Take the reciprocal of the divisor, not the dividend.
- A full fractional quotient and a count of complete pieces are different requests.
See the answer and explanation
9/10
Multiply by the reciprocal of the divisor and check by inverse multiplication. The result is 9/10.
Take it further
Compute (7/8)÷(1/4). Expected: 7/2=3 1/2; three complete pieces if only full pieces are requested.
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