A half is one of 2 equal parts. Halve a half and you get a quarter: one of 4 equal parts. Halve a quarter and you get an eighth: one of 8 equal parts. The parts must be the same size. To find a quarter of a group, halve it and then halve again. To find the whole from a part, keep doubling.
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Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- half
- one of 2 equal parts, written 1/2
- quarter
- one of 4 equal parts, written 1/4
- eighth
- one of 8 equal parts, written 1/8
Worked examples
A circle is cut into 4 equal parts and 1 part is shaded. What fraction is shaded?
- 1.The circle has 4 equal parts.
- 2.One part of 4 is one quarter.
= 1/4
What is one quarter of 12?
- 1.Halve 12: 6.
- 2.Halve again for a quarter: 3.
= 3
3 counters are one quarter of a group. How many counters are in the whole group?
- 1.Two quarters make a half: double 3 is 6.
- 2.Two halves make the whole: double 6 is 12.
= 12
For parents
Method: Repeated halving
What to say: Are all the parts the same size? How many parts make the whole?
Common mistakes:
- Compares the shaded part with the unshaded parts instead of with the whole shape (writes 1/3 for one quarter).
- Names the part that is not shaded instead of the shaded part.
- Writes the fraction upside down, with the number of parts on top (4/1 for one quarter).
- Halves once for a quarter (or twice for an eighth), stopping one halving too soon.
- Gives the number of equal groups (the denominator) instead of how many are in one group.
- Takes away one part and gives what is left instead of the part itself.
- Adds the part and the denominator to find the whole (3 is one quarter, so the whole is 3 + 4 = 7).
- Doubles the part once for any unit fraction, treating a quarter or eighth as if it were a half.
- Counts only the other parts of the whole, leaving out the part that was shown.