The idea in brief. Name the whole as the denominator's units first ("Let the number of beads be 8 units."), turn every fraction into a count of units, and then the stem's one number, whether it is what is left or the gap between two shares, is a count of units too. Price one unit from it and every other count follows.
Lesson video, with the working
Finding the whole from a fraction
4 min 29 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
In a box, 1/4 of the beads are red and 3/8 of the beads are blue. The remaining 30 beads are yellow. How many beads are there in the box?
Yellow = 1 − 1/4 − 3/8
= 8/8 − 2/8 − 3/8
= 3/8
All beads = 8 units
3 units = 30
1 unit = 30 ÷ 3 = 10
8 units = 8 × 10 = 80
There are 80 beads in the box.
Ans: 80
Example 1
1/2 of the pupils in a hall chose swimming, 1/3 of the pupils chose football and the rest chose badminton. 28 more pupils chose swimming than badminton. How many pupils were there in the hall?
Badminton = 1 − 1/2 − 1/3
= 6/6 − 3/6 − 2/6
= 1/6
All pupils = 6 units
Swimming = 3 units
Badminton = 1 unit
3 units − 1 unit = 2 units
2 units = 28
1 unit = 28 ÷ 2 = 14
6 units = 6 × 14 = 84
There were 84 pupils in the hall.
Ans: 84
How to solve it
Find the fraction measured by the given count. Yellow beads are 1 minus one quarter minus 3 eighths, which is 3 eighths.
Let all the beads be 8 units. The 30 yellow beads represent 3 units.
Find 1 unit: 30 divided by 3 is 10. The whole is 8 times 10, which is 80 beads.
For pupils, badminton is 1 minus one half minus one third, giving one sixth. Let the whole be 6 units.
Swimming is 3 units and badminton 1. Their difference of 2 units is 28 pupils, so 1 unit is 14.
The whole is 6 units: 6 times 14 is 84 pupils.
Name what the given count measures. Find one unit, then the whole.
Practice questions with worked solutions
Question 1 is free to try. The other 5 open in the free trial, each with its full working.
Question 1 of 6 · Intermediate · free to tryBala and Siti shared some marbles. Bala took 7/10 of the marbles and Siti…Bala and Siti shared some…
Bala and Siti shared some marbles. Bala took 7/10 of the marbles and Siti took the rest. Bala took 32 more marbles than Siti.
(a) How many marbles did Siti take?
(b) The marbles were bought in packets of 5 at $3 a packet. How much did all the marbles cost?
How can I help my child with finding the whole from a fraction?
Finding an unknown whole starts by identifying the fraction represented by a known amount.
What your child learns here
Finding an unknown whole starts by identifying the fraction represented by a known amount. Your child works out one equal part, then counts all the parts needed for the complete set. This subtopic applies the MOE Primary 4 understanding of fraction as part of a set in reverse. When the known amount is a remainder or a difference, its fraction must be established before the division can be chosen.
Name the whole referred to by the fractions and decide whether the stated amount is a selected part, a leftover part or a difference.
Use subtraction from one whole to express a remainder as a fraction when the other parts of that same whole are known.
Rename fractions with a common denominator before finding a difference, so the resulting units are equal-sized parts of one whole.
Divide the known amount by the number of equal parts it represents, then multiply one part by the number of parts in the whole.
Use the recovered total to answer the requested quantity, which may be another part of the collection rather than the total itself.
Does the answer make sense?
Once your child has recovered the total, find the stated fraction of that total again. It must give the known amount from the question, or the stated difference if that was the quantity used to recover the whole.
How to practise these questions
Intermediate practice recovers a whole from a difference between fractional shares, money left after spending, a fixed number given away or two groups counted together. Some questions then ask for one share or the cost of packets. Challenge questions combine a bead total with changes that leave equal colour counts, or recover an original amount from the difference between two fractional spends. Your child should identify exactly which fraction matches the known amount before finding one part and the whole. If two groups are counted together, combine their fractions only when both refer to that same original collection. If the known amount's role is unclear after the attempt, find the line in the written solution that connects it to a fraction of the whole. For the free marble-sharing question, use the written working to connect the difference in shares with the total, then check the packet count before calculating the cost.
Questions parents ask
Why does my child divide by the numerator when recovering a whole? The known amount represents the number of equal parts named by the numerator. Dividing by that number gives one part, after which the denominator tells how many parts make the complete whole. This explains the calculation without needing division by a fraction as a new procedure.
What if the question gives only the amount left? First establish what fraction of the original whole remains. If all the stated parts refer to that same whole, subtract their combined fraction from one. Your child can then treat the leftover amount as the known value of those remaining equal parts and recover the total.
How can a difference between two groups reveal the total? If both groups are fractions of the same whole, rename them with a common denominator and subtract to find the fraction represented by their difference. The given numerical difference then counts those equal parts. Finding one part allows your child to rebuild the whole or another requested group.
