In Mathematics, ratio is a way to compare two or more quantities. Ratios tell us how big one quantity is compared to another. Ratios are useful in real-life situations such as comparing prices, mixing ingredients, map scale, sharing money, and so on.
What is Ratio
A ratio compares two quantities using the symbol “ : ”
For example, if there are 6 boys and 4 girls in a class, the ratio of boys to girls is: 6:4. This means for every 6 boys, there are 4 girls.
How to express something as a ratio?
Step 1: Write the two quantities in the order stated
Example: ratio of boys to girls means boys first, girls second.
Step 2: Make sure the quantities are in the same unit
(e.g. km and m must be converted to same unit first before ratio)
Step 3: Simplify the ratio just like simplifying a fraction.
Divide both sides by the Highest Common Factor (HCF).
Example 1: Worked Example on Ratio
Amy has 24 blue beads and 36 white beads.
Express the ratio of blue beads to white beads in simplest form.
Step 1: Write the ratio as given
Blue : White
= 24 : 36
Step 2: Find the HCF of 24 and 36
HCF of 24 and 36 = 12
Step 3: Divide both numbers by 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Hence, the ratio of blue bead to white beads = 2: 3
Ratio between more than 2 quantities
So far, we have compared two quantities. But ratios can also be used to compare more than 2 quantities.
For example, 4:5:6 is a 3- term ratio. It means that for every 4 parts of the first item, there are 5 parts of the second item, and 6 parts of the third item.
Example 2: Worked Example on Ratio with more than 2 quantities
A box contains 18 red marbles, 27 blue marbles and 9 green marbles.
Express the ratio of red : blue : green marbles in simplest form.
Step 1: Write the ratio
Red : Blue : Green
= 18 : 27 : 9
Step 2: Find the HCF of all three numbers
HCF of 18, 27, and 9 = 9
Step 3: Divide all 3 terms by 9
18 ÷ 9 = 2
27 ÷ 9 = 3
9 ÷ 9 = 1
Hence, the ratio of red: blue: green marbles is 2: 3: 1