Equivalent ratios: word problems
Key notes:
Two ratios are equivalent if their cross products are equal.
Learn with an example
▶️ Are these ratios equivalent?
6 plates : 10 bowls
9 plates : 15 bowls
- yes
- no
Write the ratios as fractions.
6 / 10 and 9 / 15
Compare the two fractions to see if they are equivalent.
6 / 10 ? 9 / 15
6 × 15 = 10 × 9 Multiply both sides by 10 × 15
90 = 90 Simplify
The fractions are equivalent, so the ratios are equivalent.
▶️ Are these ratios equivalent?
8p : 3 people
3p : 2 people
- yes
- no
Write the ratios as fractions.
8 / 3 and 3 / 2
Compare the two fractions to see if they are equivalent.
8 / 3 = 3/2
8 × 2 = 3 × 3 Multiply both sides by 3 × 2
16 ≠ 9 Simplify
The cross products are not equal, so the ratios are not equivalent.
▶️ Are these ratios equivalent?
5 large necklaces : 2 small necklaces
15 large necklaces : 6 small necklaces
- yes
- no
Write the ratios as fractions.
5 / 2 and 15 / 6
Compare the two fractions to see if they are equivalent.
5 / 2 = 15 / 6
5 × 6 = 2 × 15 Multiply both sides by 2 × 6
30 = 30 Simplify
The fractions are equivalent, so the ratios are equivalent.
let’s practice! 🖊️
