Ratios and Proportions • Topic 1 of 7

Ratios

A ratio compares two quantities of the same kind, written a : b or a/b. Order matters: 3 boys to 2 girls is 3 : 2, not 2 : 3. A ratio can be scaled up or down by multiplying both parts by the same number, and is usually given in lowest terms. To split a total in a given ratio, add the parts to find how many equal shares there are, then multiply. For example, sharing $50 in the ratio 2 : 3 means 5 shares of $10, giving $20 and $30. Ratios underpin rates, mixtures and scale problems on the SAT.

✅ Solved examples

1. Simplify the ratio 12 : 18.
Divide both parts by their GCF, 6: 12 : 18 = 2 : 3.
2. In a class the ratio of boys to girls is 3 : 2. If there are 15 boys, how many girls are there?
Each "part" is 15 ÷ 3 = 5 students, so girls = 2 × 5 = 10.
3. Share $40 in the ratio 3 : 5.
Total parts = 8, so one part = $40 ÷ 8 = $5. The shares are 3×5 = $15 and 5×5 = $25.
4. Write the ratio 0.5 : 2 in whole numbers.
Multiply both by 2: 1 : 4.

✏️ Practice — try these, take hints as needed

1. Simplify the ratio 15 : 25.
Find the GCF of 15 and 25.
The GCF is 5.
Divide both parts.
3 : 5.
2. The ratio of red to blue marbles is 4 : 3. If there are 12 red, how many blue?
Find the value of one part: 12 ÷ 4.
One part = 3.
Blue = 3 × 3.
9.
3. Share 60 sweets in the ratio 1 : 2 : 3.
Total parts = 1 + 2 + 3 = 6.
One part = 60 ÷ 6 = 10.
Multiply each part by 10.
10, 20 and 30.
4. Write the ratio 1.5 : 4.5 in lowest whole-number terms.
Multiply both by 2 to clear decimals: 3 : 9.
Divide by the GCF 3.
Simplify.
1 : 3.
5. A recipe uses flour and sugar in the ratio 5 : 2. With 10 cups of flour, how much sugar?
One part = 10 ÷ 5 = 2 cups.
Sugar = 2 parts.
Multiply.
4 cups.

📝 Topic test — 8 questions

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