A ratio compares two quantities. Drag the sliders and watch two quantities simplify to their ratio in real time.
Try it: set both sliders to make a 1:1 ratio!
A ratio compares two quantities of the same kind, showing how many times one contains the other. We write a ratio using a colon: a : b. Order matters — 3 : 5 is not the same as 5 : 3.
Simplify the ratio 12 : 18. The HCF of 12 and 18 is 6. Divide both terms by 6: 2 : 3
Simplify 5 : 9. Since the HCF of 5 and 9 is 1, this ratio is already in its simplest form: 5 : 9
Equivalent ratios represent the same comparison, made by multiplying or dividing both terms by the same number — just like equivalent fractions.
2 : 3 → (×4) → 8 : 12. Both are equivalent ratios.
10 : 15 → (÷5) → 2 : 3. Both are equivalent ratios.
If 2 : 3 = 8 : 12, we say these four numbers are in proportion, written as 2 : 3 :: 8 : 12. Check by cross-multiplying: 2 × 12 = 24, and 3 × 8 = 24 — they match, so it's a true proportion
Find x if 3 : 4 = 9 : x. Cross-multiply: 3 × x = 4 × 9, so 3x = 36, and x = 12
Answer 3 out of 4 correctly to complete this quest and unlock Algebra Isle.
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