Divide a Unit Fraction into Equal Shares
Partition the supplied unit fraction into the stated number of equal pieces.
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: Share 1/4 of a strip equally among three people.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Dividing a unit fraction by a whole number makes smaller equal parts of that fraction. If one third is shared among four recipients, each receives one twelfth of the original whole. The denominator grows because the whole would contain more of these smaller pieces. Multiplication checks the share.
Partition the supplied unit fraction into the stated number of equal pieces. Record the new fraction of the original whole. Multiply by the recipient count to check that all shares reconstruct the starting unit fraction.
Keep the original whole as the fraction reference. The share is smaller than the starting unit fraction, not three times larger. Draw one whole subdivided into the starting denominator, then split its selected part again.
- Draw one whole subdivided into the starting denominator, then split its selected part again.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Partition the supplied unit fraction into the stated number of equal pieces.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
Share 1/4 of a strip equally among three people. Split that quarter into three equal pieces. Each is 1/12 of the full strip because four quarters each contain three such pieces. Check 3×1/12=1/4; each share is smaller than the original quarter. Keep the original whole as the fraction reference. The share is smaller than the starting unit fraction, not three times larger. Draw one whole subdivided into the starting denominator, then split its selected part again.
Check your reasoning
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Helpful tips
- Keep the original whole as the fraction reference.
- The share is smaller than the starting unit fraction, not three times larger.
See the answer and explanation
1/6
Divide the unit fraction into three smaller equal parts. The result is 1/6.
Take it further
Share 1/5 of a whole among four people: 1/20 each. Then make a line plot for supplied measurements 1/8,1/8,1/4,1/2 L. Expected marks: two at 1/8, one at 1/4, one at 1/2. Total volume is 1 L; redistributed equally across all four observations, each share is 1/4 L.
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More practice: try new cases
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Check the subject sources
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