Ratio and proportion
Proportion
Proportion compares a part with the WHOLE. That one difference is what separates it from ratio.
Part of the whole
PROPORTION compares one part with the TOTAL. It is usually written as a fraction or a percentage. A bag has 2 orange, 3 blue and 5 green counters — 10 altogether. The proportion that are blue is 3 out of 10 = 3/10 = 30%.
Ratio or proportion?
This is the distinction to hold on to: RATIO compares part with PART. Blue to green is 3 : 5. PROPORTION compares part with WHOLE. Blue is 3 out of 10. Same counters, two different questions. Read carefully which one is being asked.
Working out a proportion
1. Count the part you want. 2. Count the total. 3. Write it as a fraction, then simplify or convert to a percentage. Zara has 10 blue pens and 5 red — 15 altogether. The proportion that are red is 5/15 = 1/3. Notice that is NOT 50%, even though there are half as many red as blue. Comparing red with blue gives a ratio; comparing red with the total gives the proportion.
As a percentage
To turn a proportion into a percentage, write it as a fraction of 100. 3 out of 10 = 30/100 = 30% 1 out of 4 = 25/100 = 25% Percentages make different proportions easy to compare, because they are all out of the same number.
Worked examples
The proportion that are blue
- The bag has 2 + 3 + 5 = 10 counters.
- 3 of them are blue.
- 3 out of 10 is 3/10.
Answer: 3/10, or 30%
The proportion that are red
- Zara has 10 blue and 5 red — 15 in total.
- 5 of the 15 are red.
- 5/15 simplifies to 1/3.
Answer: 1/3 of the pens are red
Why it is not 50%
- There are half as many red as blue, so the RATIO is 1 : 2.
- But the proportion compares red with the total of 15, not with the blue.
Answer: 1/3, not 50%
Ratio or proportion?
- 'The ratio of black to white' compares part with part.
- 'What proportion are black' compares part with the whole.
Answer: Ratio: part to part. Proportion: part to whole
Turning a proportion into a percentage
- 1 in every 4 squares is black.
- 1/4 = 25/100.
Answer: 25%
Where you see this in real life
- A survey saying 30% of people chose blue — a proportion of everyone asked.
- A juice labelled '20% real fruit' — 20 parts out of every 100.
- Working out what fraction of your class walks to school.
Key words
- Proportion
- A comparison of a part with the whole.
- Ratio
- A comparison of one part with another part.
- Fraction
- A part of a whole, written with a numerator and denominator.
- Percentage
- A proportion written out of 100.
- Total
- The whole amount, found by adding all the parts.
- Simplify
- Cancel a fraction to its smallest form.