Share $84 in the ratio 2 : 5.
- There are 7 ratio units.
- Each unit is $84 ÷ 7 = $12.
- The shares are $24 and $60. Check: 24 + 60 = 84; 24 : 60 = 2 : 5.
Sharing in a ratio
A ratio gives parts; the total gives their size.
Count the equal ratio units
To share 40 counters in a 3 : 5 ratio, there are 3 + 5 = 8 equal ratio units. Each unit is 40 ÷ 8 = 5 counters. The shares are 15 and 25.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
The whole is not one of the shares
A 3 : 5 split means the first share is 3/8 of the total and the second is 5/8. Use the sum of all terms, including a third category if present.
Respect indivisible objects
A mathematical split may produce decimal shares. Money and measured lengths can allow fractional units, but whole people or objects may require a different total or an explicitly approximate allocation.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
Worked examples
Split 36 m of ribbon among three groups in the ratio 1 : 2 : 3.
- There are 6 equal ratio units.
- One unit is 36 ÷ 6 = 6 m.
- The lengths are 6 m, 12 m and 18 m.
Try it before checking.
Divide 48 tokens in the ratio 1 : 3. What is the smaller share?
A first hint
There are 4 equal ratio units.
Compare your reasoning
48 ÷ 4 = 12 tokens for the smaller share; the other share is 36.
Practise the skill.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Explain a little more.
Can 25 students be split exactly in a 2 : 3 ratio? What about a 3 : 4 ratio?
Use this thinking in the If… project →