The idea in brief. Find the whole first. One sector's count and the fraction it is of the circle give the total, and once the total is known every other sector is either a fraction of it or what is left of it.
Lesson video, with the working
Finding the whole from a pie chart
4 min 04 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
The pie chart shows the number of shells of each kind that Priya collected at the beach. The part representing the cowrie shells is marked with a right angle.
(a) How many shells did Priya collect altogether?
(b) How many scallop shells did she collect?
from the pie chart, 45 of the shells are cowrie shells, 75 are clam shells and 36 are snail shells
the right angle shows that 1/4 of the shells are cowrie shells
total = 45 × 4 = 180
scallop shells = 180 − 45 − 75 − 36 = 24
Ans: (a) 180 (b) 24
Example 1
The pie chart shows the number of packets of noodles of each flavour a shop sold in a week. The parts representing curry noodles and tom yam noodles together make one half of the chart, and the part representing chicken noodles is marked with a right angle. How many packets of mushroom noodles did the shop sell?
from the pie chart, the shop sold 120 packets of curry noodles and 96 packets of chicken noodles, and 1/12 of the packets were prawn noodles
the right angle shows that the 96 packets of chicken noodles are 1/4 of the packets
total = 96 × 4 = 384
The shop sold 384 packets altogether.
curry and tom yam = 384 ÷ 2 = 192
tom yam = 192 − 120 = 72
prawn = 384 ÷ 12 = 32
mushroom = 384 − 120 − 72 − 96 − 32 = 64
Ans: 64
How to solve it
Use the marked quarter to find the whole. 45 cowrie shells make one quarter, so 45 times 4 is 180 shells.
Subtract the other kinds: 180 minus 45 minus 75 minus 36 is 24 scallop shells.
In the noodle chart, chicken is one quarter. 96 times 4 is 384 packets altogether.
Curry and tom yam make one half: 384 divided by 2 is 192. Tom yam is 192 minus 120, which is 72.
Prawn is one twelfth: 384 divided by 12 is 32 packets.
Subtract every known flavour: 384 minus 120 minus 72 minus 96 minus 32 is 64 mushroom packets.
Find the whole from the marked quarter first. Then find every missing part in order.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
Question 1 of 7 · Intermediate · free to tryThe pie chart shows how Devi uses her monthly allowance. She spends $45 on…The pie chart shows how Devi…
The pie chart shows how Devi uses her monthly allowance. She spends $45 on books each month, and the part representing books is marked with a right angle. How much is Devi's monthly allowance?
the right angle shows that the $45 she spends on books is 1/4 of her allowance
1 unit = $45
4 units = 4 × $45 = $180
Answer: $180
For parents
How can my child find pie chart totals from one sector?
A sector's fraction and its number of objects together can reveal the total represented by a pie chart.
What your child learns here
A sector's fraction and its number of objects together can reveal the total represented by a pie chart. Your child treats that sector as a known number of equal parts, finds one part and rebuilds the whole. This page applies the MOE Primary 4 outcome on interpreting pie charts alongside fraction as part of a set. Some questions provide a difference between sectors instead of a single sector's count.
Match the stated count to the correct sector and its fraction before using either number in a calculation.
Divide a known sector's count by its numerator to find one equal part, then multiply by its denominator to obtain the complete total.
Calculate another sector's count from its share of the recovered total, keeping the chart's categories distinct in the working.
When the difference between sectors is given, subtract their fractions of the same whole to identify the share represented by that difference.
Read any accompanying table as further information about the chart, checking whether its values represent individual categories or the complete group.
Does the answer make sense?
Find the original known sector's fraction of your child's calculated total. It must reproduce the supplied sector count exactly, and a total for a chart with other non-empty categories must be larger than that count.
How to practise these questions
The Intermediate questions recover a total from a known quarter or from the other three quarters, then may ask for a missing category or the money collected from it. Challenge questions link monthly spending with a pie chart or combine equal sectors with a half-circle relationship. Your child should first identify the fraction represented by the known amount, rather than assume that any labelled sector is one quarter. After finding the whole, reread the question to see whether another category, a cost or a later savings fraction is required. After checking the written solution, pause at the recovered total and ask your child to explain which share established it. On the free allowance card, the written working connects the right-angle sector with one quarter of the allowance and uses its value to recover the monthly total.
Questions parents ask
Why is the given number beside a sector not necessarily the total? A label attached to one sector usually counts that category. The chart's title or question tells your child what the whole circle represents. Read the sentence containing the number, then identify the matching sector before deciding whether the value describes a part or the full collection.
How can a difference between two sectors give the whole? Both sectors are fractions of the same total, so their difference is also a fraction of that total. Your child first finds that fractional difference using equal-sized parts. The given count then represents those parts, allowing one part and the complete total to be found.
When should my child stop after finding the pie chart total? Only when the total is what the question requests. Another category, a difference or a combined group may still be required. Ask your child to compare the final answer label with the question's final sentence; the recovered total may be a useful intermediate result rather than the answer.
