Year 5 Maths | Learn, see, try
Different fraction names can show the same amount
One half and three sixths can cover exactly the same amount of a whole. They are equivalent fractions. The names change because the whole has been divided into different numbers of equal pieces, not because the amount has grown.
What to notice
Use wholes of the same size. Half of a large sandwich and half of a small sandwich share a fraction name but are not equal-sized servings. Fraction-bar comparisons below keep the whole length fixed.
What to do
Split every original part into the same number of smaller pieces. Multiply both numerator and denominator by that number. To simplify, divide both by a common factor instead.
Why it works
Cutting each half into three pieces turns two halves into six equal pieces overall. The one marked half becomes three marked pieces. The marked area stays in the same place, so 1/2 = 3/6.
Work through an example
Show why 1/2 and 3/6 are equivalent.
- Start with one of two equal parts marked.
- Divide each half into three equal pieces, making six pieces altogether.
- Three of the six are marked. Both bars cover the same length.
A common mistake
Changing only the denominator changes the fraction. 1/2 is not 1/6: a sixth is a smaller piece and only one is counted. Both numbers must change by the same multiplication or division factor.
A strategy to try
Ask “What happened to the denominator?” If it doubled, double the numerator too. Then estimate: a fraction that was more than one half should still be more than one half after you rename it.
Try it now
Try three questions
No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.
For parents and carers
Fold two same-sized paper strips, one into halves and another into sixths. Lining up the marked lengths makes equivalence visible before introducing a written calculation. Avoid treating “multiply top and bottom” as a trick without a model.
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