The idea in brief. Draw all three bars and make every one of them whole units before you share anything. A piece MORE comes off the total; a piece LESS goes back on to it, drawn dashed on the short bar. Only then does the total price the units, and the answer is read from the bar the question asked about, with its own piece put back.
Lesson video, with the working
Three quantities compared
4 min 36 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
A school library has 2674 books in English, Chinese and Malay. There are 3 times as many English books as Malay books. There are 259 fewer Chinese books than English books. How many Chinese books are there?
7 units = 2674 + 259 = 2933
1 unit = 2933 ÷ 7 = 419
3 units = 3 × 419 = 1257
Chinese books = 1257 − 259 = 998 books
Ans: 998 books
Example 1
Boxes A, B and C hold 3240 paper clips altogether. Box B holds twice as many paper clips as Box A. Box C holds 315 more paper clips than Box B. How many paper clips does Box C hold?
5 units = 3240 − 315 = 2925
1 unit = 2925 ÷ 5 = 585
2 units = 2 × 585 = 1170
Box C = 1170 + 315 = 1485 paper clips
Ans: 1485 paper clips
How to solve it
Choose one unit and express the other quantities using it. Malay books are 1 unit, English 3, and Chinese 3 units minus 259.
Add the missing part to make equal units: 2674 plus 259 is 2933, representing 7 units.
Find 1 unit: 2933 divided by 7 is 419. Then 3 units are 3 times 419, which is 1257.
Subtract the part added: 1257 minus 259 is 998 Chinese books.
If there is an extra part instead, subtract it from the total. For the boxes, 3240 minus 315 is 2925 for 5 units.
Find the units, then restore the extra part: 2925 divided by 5 is 585; 2 times 585 plus 315 is 1485 paper clips.
Make whole units first. Then find the quantity the question asks for.
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 tryA shop sold red, blue and green balloons. It sold twice as many blue…A shop sold red, blue and green…
A shop sold red, blue and green balloons. It sold twice as many blue balloons as red ones, and twice as many green balloons as blue ones. It sold 1236 more green balloons than red ones. How many balloons did it sell altogether?
How can I help my child organise P4 three-quantity problems?
Your child combines relationships among three quantities to find unknown amounts.
What your child learns here
Your child combines relationships among three quantities to find unknown amounts. This page applies the mathematics curriculum's problem-solving framework using Primary 4 whole-number calculations. There is no separate content outcome called three-quantity problems. The focus is choosing a common reference quantity and keeping each comparison attached to the correct pair.
Identify which two quantities each statement compares, and avoid treating a relationship between one pair as if it applied to all three.
Choose an amount that can serve as a common unit when one quantity is described as several times another.
Account for a stated extra amount or shortfall before dividing a total into equal units, explaining how the adjusted total was obtained.
Distinguish a total of all three quantities from a pair total, especially when a quantity appears in more than one given comparison.
Find the requested amount from the unit value, then recover the other quantities as needed to check the complete set of relationships.
Does the answer make sense?
After finding the three amounts, your child can add them and compare the sum with the total given in the question. Each stated pair comparison must hold too, so a correct sum cannot by itself confirm that the amounts have been assigned to the right people or groups.
How to practise these questions
Intermediate practice includes chains of multiplicative comparisons, a quantity compared with a pair total, a fixed shortfall and overlapping pair totals. Challenge questions combine a fixed difference with a multiple, either to compare the outer quantities or to recover one class's collection from a total across three classes. There are no Basic questions here. Ask your child to name the two quantities in each relationship before combining information. A statement about twice a pair's total includes both members of that pair, which affects the unit count. After recovering the amounts, check every pair total or comparison given. The requested difference or total should then be calculated from those verified quantities.
Questions parents ask
Where should my child begin when three amounts are unknown? Begin with the relationships rather than trying to guess the amounts. Ask which quantity is used to describe another, and whether the remaining comparison can use that same reference. This often reveals a common unit and any fixed extra amount that needs separate attention.
Why might a total need adjusting before division? A total may include equal units together with a fixed extra amount, or it may be short of a complete set of units. Your child needs to identify that difference and explain whether to add or subtract it. Only the resulting equal-unit total can be divided directly.
What can I ask when my child loses track of the three quantities? Ask your child to say one comparison using the quantities' names, then the next comparison separately. Return to the sentence that supplies the total and identify exactly whose amounts it includes. This keeps the relationships manageable without changing the information in the problem.
