Proportion Calculator: Solve a/b = c/d & Find x Fast

What does x = 9 mean?

It means 3/4 and 9/12 are the same proportion — three quarters of 12 is 9, just as three quarters of 4 is 3. The missing term, the ratio and the percent are three outputs, never the same number: the missing term is the answer, the ratio 3:4 is the proportion in lowest terms, and 75.00% is the same fraction out of a hundred. A proportion says two fractions are equal, so whatever you do to one side you do to the other, and the missing term is the number that keeps them equal.

Three things to check before you trust the number

Cross-multiply, then divide. The missing term is the first term times the fourth term, divided by the second term: 3 times 12 is 36, and 36 divided by 4 is 9. If the answer does not check — 9 over 12 is 3 over 4, simplified — the proportion is wrong.

The ratio is the proportion in lowest terms. 3:4 stays 3:4, but 6:8 becomes 3:4, and 9:12 becomes 3:4 too — the same proportion in different clothes. If the ratio does not simplify to the same pair, the two fractions are not a proportion.

A zero underneath is not a number. A fraction with a zero underneath has no value, so the calculator says so plainly instead of giving you a number you cannot use. A zero on top is fine — it gives x = 0.

Worked example

On the defaults: 3/4 = x/12.

1. Cross-multiply: 3 × 12 = 36, and 4 × x = 4x.
2. Set them equal: 4x = 36.
3. Divide by 4: x = 36 ÷ 4 = 9.
4. Check: 9 ÷ 12 = 0.75, and 3 ÷ 4 = 0.75 — the same, so the proportion holds.
5. Ratio: 3:4 is already in lowest terms.
6. As a percent: 3 ÷ 4 × 100 = 75.00%.
7. Smallest fourth term for x of at least 10: 13.5 — at 13.5 x is 10.13 (unrounded 10.125000), and at 13 it is 9.75.
8. Smallest fourth term for x of at least 12: 16 — at 16 x is 12.00, and at 15 it is 11.25.

Every branch, checked

• 1/2 = x/10: 1/2 = x/10: x = 5.00; ratio 1:2; 50.00%. 1/2 = x/10 — x is 5.00, half of 10.
• 2/5 = x/15: 2/5 = x/15: x = 6.00; ratio 2:5; 40.00%. 2/5 = x/15 — x is 6.00, two fifths of 15.
• 5/8 = x/24: 5/8 = x/24: x = 15.00; ratio 5:8; 62.50%. 5/8 = x/24 — x is 15.00, five eighths of 24.
• 7/10 = x/35: 7/10 = x/35: x = 24.50; ratio 7:10; 70.00%. 7/10 = x/35 — x is 24.50, seven tenths of 35.
• 3/7 = x/21: 3/7 = x/21: x = 9.00; ratio 3:7; 42.86%. 3/7 = x/21 — x is 9.00, 42.86% — three sevenths of 21.
• 9/12 = x/36: 9/12 = x/36: x = 27.00; ratio 3:4; 75.00%. 9/12 = x/36 — x is 27.00, nine twelfths of 36.
• 4/9 = x/27: 4/9 = x/27: x = 12.00; ratio 4:9; 44.44%. 4/9 = x/27 — x is 12.00, 44.44% — four ninths of 27.
• 11/20 = x/100: 11/20 = x/100: x = 55.00; ratio 11:20; 55.00%. 11/20 = x/100 — x is 55.00, eleven twentieths of 100.
• 2.5/4 = x/16: 2.5/4 = x/16: x = 10.00; ratio 5:8; 62.50%. 2.5/4 = x/16 — x is 10.00, the ratio 2.5:4 is 5:8.
• 1/3 = x/9: 1/3 = x/9: x = 3.00; ratio 1:3; 33.33%. 1/3 = x/9 — x is 3.00, 33.33% — a third of 9.

The reverses, worked backwards

• Smallest fourth term for x to REACH at least 10: 13.5 — at 13.5 the figures are x = 10.13 (unrounded 10.125000); ratio 3:4; 75.00% (unrounded 75.000000); at the lower neighbor the figures are x = 9.75 (unrounded 9.750000); ratio 3:4; 75.00% (unrounded 75.000000); at the upper neighbor the figures are x = 10.50 (unrounded 10.500000); ratio 3:4; 75.00% (unrounded 75.000000) — verdict: STEP.
• Smallest fourth term for x to REACH at least 12: 16 — at 16 the figures are x = 12.00 (unrounded 12.000000); ratio 3:4; 75.00% (unrounded 75.000000); at the lower neighbor the figures are x = 11.25 (unrounded 11.250000); ratio 3:4; 75.00% (unrounded 75.000000); at the upper neighbor the figures are x = 12.75 (unrounded 12.750000); ratio 3:4; 75.00% (unrounded 75.000000) — verdict: STEP.
• Largest first term for x to STAY at or below 6: 2 — at 2 the figures are x = 6.00 (unrounded 6.000000); ratio 1:2; 50.00% (unrounded 50.000000); at the upper neighbor the figures are x = 7.50 (unrounded 7.500000); ratio 5:8; 62.50% (unrounded 62.500000); at the lower neighbor the figures are x = 4.50 (unrounded 4.500000); ratio 3:8; 37.50% (unrounded 37.500000) — verdict: STEP.
• Largest fourth term for x to STAY at or below 20: 26 — at 26 the figures are x = 19.50 (unrounded 19.500000); ratio 3:4; 75.00% (unrounded 75.000000); at the upper neighbor the figures are x = 20.25 (unrounded 20.250000); ratio 3:4; 75.00% (unrounded 75.000000); at the lower neighbor the figures are x = 18.75 (unrounded 18.750000); ratio 3:4; 75.00% (unrounded 75.000000) — verdict: STEP.
• Largest second term for x to REACH at least 15: 2 — at 2 the figures are x = 18.00 (unrounded 18.000000); ratio 3:2; 150.00% (unrounded 150.000000); at the lower neighbor the figures are x = 14.40 (unrounded 14.400000); ratio 6:5; 120.00% (unrounded 120.000000); at the upper neighbor the figures are x = 24.00 (unrounded 24.000000); ratio 2:1; 200.00% (unrounded 200.000000) — verdict: STEP.
• Smallest first term for x to REACH at least 8: 3 — at 3 the figures are x = 9.00 (unrounded 9.000000); ratio 3:4; 75.00% (unrounded 75.000000); at the lower neighbor the figures are x = 6.00 (unrounded 6.000000); ratio 1:2; 50.00% (unrounded 50.000000); at the upper neighbor the figures are x = 12.00 (unrounded 12.000000); ratio 1:1; 100.00% (unrounded 100.000000) — verdict: STEP.

What the defaults assume

The defaults are 3/4 = x/12 — three quarters, the most common proportion in everyday life — and the answer is 9, the ratio 3:4 and 75.00%. They are a starting point, not a benchmark: your proportion may be 2/5 or 7/10, and the right answer for you is the one your numbers describe. Change the three terms to your own and the calculator recomputes instantly. Cross-multiply, then divide — and check that the two fractions are equal when you are done.

These notes repeat in every explainer section because this page is built to be read start to finish: the defaults are one proportion, not a standard; cross-multiply, then divide; the ratio is the proportion in lowest terms; and a zero underneath is not a number.

Output · formula · meaning

Who uses this

• A cook scaling a recipe — 3 cups of flour to 4 cups of milk, and 12 cups of milk needs 9 cups of flour.
• A student checking homework — 3/4 = x/12 gives x = 9, by cross-multiplication, not by guessing.
• A builder mixing concrete — a 1:2 ratio of cement to sand, and 10 bags of cement needs 20 bags of sand.
• A shopper comparing unit prices — 3 for $4 and 12 for $16 is the same deal, because 3/4 and 12/16 are the same proportion.

Accuracy & limitations

The calculator does the arithmetic exactly — the missing term is the first term times the fourth term over the second term, the ratio is divided by the greatest common divisor, and the percent is the first term over the second term times a hundred — and every figure on this page is checked against an independent model. What it cannot do is decide which number is missing: it solves for the fourth term, x, in a/b = x/d, so if your unknown is the first term, solve it as a proportion the other way round, or swap the fractions. It also takes one proportion at a time — a chain of three ratios needs the ratio-simplifier page or two proportions, not one. And the missing term is 10.13, unrounded 10.125000, on a fourth term of 13.5 — the page prints the unrounded figure so the rounding does not mislead you.

Cite this calculator

A proportion a/b = x/d is solved by cross-multiplication: x is a times d over b. On the defaults — 3/4 = x/12 — the missing term is 9, the ratio 3:4, and 75.00%. Smallest fourth term for x to reach at least 10: 13.5. Smallest fourth term for x to reach at least 12: 16. Largest first term for x to stay at or below 6: 2. Largest fourth term for x to stay at or below 20: 26. Largest second term for x to reach at least 15: 2. Smallest first term for x to reach at least 8: 3. Source: Bright Side Kit, brightoolbox.com.

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