Primary 6 maths · Ratio, rate & percentage · About 12 minutes
Dividing a quantity in a ratio
Find the value of one unit from a total
Start the interactive lesson →Open practice activity
What you will learn
- Find the value of one unit from a total
- Divide a quantity in a given ratio
- Use the difference in units to find a total
Models used: ratio bar models, bar models, stories.
Before you start
One unit is the key
Red has 2 equal units. Blue has 3 of the same units.
A small box represents one equal unit. Read the number inside to find the value of that unit.
Red has 2 equal units. Blue has 3 of the same units.
red : blue = 2 : 3
Keep the number of units separate from the value of one unit. Multiplying them gives the amount in that row.
A small box represents one equal unit. Read the number inside to find the value of that unit.
Together they have five units. If there are 20 counters, each unit is 4 counters.
20 ÷ 5 = 4
Keep the number of units separate from the value of one unit. Multiplying them gives the amount in that row.
A small box represents one equal unit. Read the number inside to find the value of that unit.
Red gets 8 counters. Blue gets 12. Their shares still have the ratio 2 to 3.
2 × 4 = 8; 3 × 4 = 12
Keep the number of units separate from the value of one unit. Multiplying them gives the amount in that row.
Why does the difference method work?
If Ali has 3 units and Ben has 2, Ali has exactly 1 unit more. So an extra $12 means one unit is $12, and every share can be worked out from that. The bars make the extra unit easy to see.
Ali : Ben = 3 : 2
Worked example
$63 is shared in the ratio 4 : 3. How much is the larger share?
Count the units.
4 + 3 = 7 units
How many units altogether?
7
Find one unit.
63 ÷ 7 = 9
What is one unit worth?
9
The larger share has 4 units.
4 × 9 = 36
Larger999936 altogetherSmaller99927 altogetherLarger : Smaller = 4 : 3 · 7 units = 63 · 1 unit = 9
So the larger share is $36.
36 + 27 = 63 ✓
Common mistakes to discuss
- Dividing the total by one part of the ratio. For 3 : 2 and a total of 40, divide by the number of units (5), not by 3 or 2.
- Using the total when only the difference is known. If one person gets $12 more, that $12 matches the difference in units, not the whole amount.
Check your understanding
- share $40 between two people in the ratio 3 : 2
- find one unit when the total or the difference is known
- draw a bar model for a ratio problem
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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