Rename Before Subtracting
Subtract unlike fractions by finding a shared part size.
Supplied materials
- Paper and pencil.
- Supplied pretend strip length: 5/6 meter; a 1/4-meter part is removed.
Learn the idea
To remove a quarter-meter from a length measured in sixths, first express both lengths in the same unit fraction. Twelfths work because each sixth splits into two twelfths and each quarter splits into three twelfths.
Rename the amounts without changing their lengths, then subtract the counts of twelfths. The remainder should be shorter than the starting strip but positive here. Add the removed length back as a check.
- Write 5/6 = 10/12 and 1/4 = 3/12.
- Remove three twelfth-parts from ten to find seven.
- Check 7/12 + 3/12 = 10/12, then subtract 1/6 from 3/4.
See the method in action
5/6 − 1/4 = 10/12 − 3/12 = 7/12 meter. Adding the removed 3/12 back gives 10/12 = 5/6.
Check your reasoning
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See the answer and explanation
7/12
3/4 = 9/12 and 1/6 = 2/12. Subtracting leaves 7/12. It is less than 3/4, as a positive amount was removed.
Take it further
Remove 1/3 from 3/4 instead. Rename 1/3 as 4/12; 9/12 − 4/12 = 5/12. The larger removed amount leaves a smaller remainder.
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