Ratio and proportion
Ratio
Ratio compares one part with another part. Get the order right — 2:3 and 3:2 describe very different situations.
What a ratio is
A RATIO compares one group with another. It is written with a colon. In a bag with 2 orange, 3 blue and 5 green counters: orange : blue : green = 2 : 3 : 5 A ratio compares PART with PART. It does not tell you the total directly.
The order matters
Write the numbers in the order the question names them. orange : blue : green = 2 : 3 : 5 blue : green : orange = 3 : 5 : 2 green : blue : orange = 5 : 3 : 2 Same counters, three different-looking answers — all correct, because the labels changed order too. Zara has 10 blue pens and 5 red. The ratio of RED to BLUE is 5 : 10, not 10 : 5. Read carefully which comes first.
'For every' language
A ratio can be read as 'for every'. A ratio of 1 : 3 black to white means: for every 1 black square there are 3 white ones. That also means 1 in every 4 squares is black — because 1 + 3 = 4 squares in each group. Notice the difference between '1 to 3' and '1 in 4'; mixing them up is a very common error.
Simplifying a ratio
Divide both parts by the same number, just like a fraction. 10 : 5 both divide by 5, giving 2 : 1. So 10 blue pens to 5 red is the same ratio as 2 blue to 1 red — for every 2 blue pens there is 1 red one.
Worked examples
Writing a ratio in order
- The bag has 2 orange, 3 blue and 5 green.
- Write them in the order asked: orange : blue : green.
Answer: 2 : 3 : 5
Changing the order
- The same bag, but asked as blue : green : orange.
- Blue is 3, green is 5, orange is 2.
Answer: 3 : 5 : 2
Red pens to blue pens
- Zara has 10 blue and 5 red.
- The question asks red first, then blue.
Answer: 5 : 10, which simplifies to 1 : 2
From ratio to 'one in every'
- The ratio of black to white is 1 : 3.
- Each group has 1 + 3 = 4 squares.
- One of those four is black.
Answer: 1 in every 4 squares is black
Simplifying 10 : 5
- Both numbers divide by 5.
- 10 ÷ 5 = 2 and 5 ÷ 5 = 1.
Answer: 2 : 1
Where you see this in real life
- A recipe using flour and butter in the ratio 2 : 1.
- Mixing squash and water in the ratio 1 : 4.
- A class with a ratio of 3 girls to 2 boys.
Key words
- Ratio
- A comparison of one part with another, written with a colon.
- Part
- One of the groups being compared.
- Simplify
- Divide both parts by the same number.
- For every
- The phrase used to read a ratio aloud.
- Colon (:)
- The symbol separating the parts of a ratio.
- Order
- Which part is named first — it changes the answer.