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Simplify a ratio, solve a proportion, or compare two - with every step.
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The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
A ratio compares two quantities by division: 12 : 8 says the first is one and a half times the second. Multiply or divide BOTH parts by the same number and the comparison has not changed - 12 : 8, 6 : 4 and 3 : 2 are the same ratio in different clothes. Simplifying just means dividing both parts by their greatest common factor until nothing is shared, exactly like reducing a fraction.
A proportion is a claim that two ratios are equal - 3 : 4 = 9 : x - and one fact unlocks every such problem: in a true proportion the cross products match. Multiply along the two diagonals; the products are equal, so an unknown anywhere in the four positions is one multiplication and one division away. That is cross multiplication, and this page writes it out rather than just landing on x = 12.
Decimals and fractions are welcome and are cleared first, exactly: 2.5 : 1.5 scales to 25 : 15 and then to 5 : 3, and a missing value of 35/3 is given as 35/3 - never as 11.67, because a rounded answer to an exact question is a different answer.
Multiply both parts by the same number until both are whole: 2.5 : 1.5 becomes 25 : 15 (times 10). Scaling both parts together never changes the ratio.
The largest number dividing both parts. For 25 and 15 it is 5.
25 ÷ 5 = 5 and 15 ÷ 5 = 3, so the ratio is 5 : 3 in lowest terms. If the greatest common factor is 1, it already was.
Write the proportion with x in its place - 3 : 4 = 9 : x is 3/4 = 9/x - multiply along the diagonals to get 3x = 36, and divide: x = 12.
The same comparison in its common costumes: lowest terms, fraction, 1 : n, and the first part's share of the whole.
| Ratio | Lowest terms | As a fraction | Share of the whole |
|---|---|---|---|
| 12 : 8 | 3 : 2 | 3/2 | 60% |
| 2 : 4 | 1 : 2 | 1/2 | 33⅓% |
| 25 : 15 | 5 : 3 | 5/3 | 62.5% |
| 6 : 9 | 2 : 3 | 2/3 | 40% |
| 10 : 4 | 5 : 2 | 5/2 | 71³⁄₇% |
| 2.5 : 1.5 | 5 : 3 | 5/3 | 62.5% |
| 1/2 : 3/4 | 2 : 3 | 2/3 | 40% |
| 7 : 7 | 1 : 1 | 1 | 50% |
12 : 8The greatest common factor of 12 and 8 is 4, so divide both parts by it: 3 : 2. As a fraction that is 3/2, as a decimal 1.5, and as shares of the whole the first part takes 3 of every 5, which is 60%. One division, four readings.
2.5 : 1.5Multiply both parts by 10 to get 25 : 15 - allowed, because scaling both parts together is exactly what a ratio ignores - then divide by the greatest common factor 5 to reach 5 : 3. Two steps, both shown, and no floating point anywhere.
3 : 4 = 9 : ?Cross multiply: 3 · x = 4 · 9, so 3x = 36 and x = 12. The check is built into the method - 9 : 12 reduces to 3 : 4, the ratio you started with. Leave any one of the four boxes empty and the same two moves find it.
1 : 2 = 3 : 6Cross multiply both diagonals: 1 · 6 = 6 and 2 · 3 = 6. They match, so yes - the two are the same comparison at different scales. If the products had differed, the verdict would be no, and the two reduced forms would show by how much.
