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Proportion Calculator

Enter three of the four values in A/B = C/D and leave the fourth blank. The missing value appears with the full cross-multiplication working.

Your proportion

A/B = C/D. Fill in three terms and leave the fourth blank to solve for it.
Proportion
7/12 = x/96
Method
Cross-multiply: A × D = B × C
Missing term C
56
Completed proportion
7/12 = 56/96
Cross products
672 and 672
Ratio as a decimal
0.5833
Scale factor
×8
Write the proportion
7/12 = x/96
Cross-multiply
7 × 96 = 12 × x
Multiply out
12x = 672
Divide both sides by 12
x = 672 ÷ 12 = 56
Check
7/12 = 56/96

How to use this calculator

  1. Enter the first fraction as A over B — the two values you already know.
  2. Enter whichever part of the second fraction you know, and leave the unknown one blank. Any of the four terms can be the blank.
  3. Read the missing value above the supporting figures, then open the working panel for the cross-multiplication line by line.

The cross products are worth a glance whenever an answer looks wrong. When the proportion is correct, the two products match exactly — if they do not, one of the three entries is not what you meant.

How to solve a proportion

A proportion says two fractions are equal. Multiplying each numerator by the opposite denominator turns that statement into a straightforward equation.

A/B = C/D means A × D = B × C
  • A, B — the first fraction, e.g. 7 and 12
  • C, D — the second fraction, e.g. x and 96
  • x — whichever term was left blank
Solving 7/12 = x/96 step by step
StepWorking
Write the proportion7/12 = x/96
Cross-multiply7 × 96 = 12 × x
Multiply out12x = 672
Divide both sides by 12x = 672 ÷ 12 = 56
Check7/12 = 56/96

The same four lines solve any proportion, wherever the blank sits. Only the division at the end changes: divide by whichever number ended up multiplied by x.

Where proportions are used

  • Scaling recipes — 7 people out of a 12-person recipe, applied to 96 grams of an ingredient.
  • Map and model scales — 1 cm on a 1:25,000 map covers 25,000 cm on the ground.
  • Unit pricing — if 12 items cost £7, a proportion gives the price of 96.
  • Medicine and mixtures — a dose per kilogram, applied to a body weight.
  • Similar triangles — corresponding sides of similar shapes are always in proportion, which is how heights are measured from shadows.

All five are the same sum. Whatever the units, if two quantities rise and fall together at a fixed rate, three known values give the fourth.

Frequently asked questions

How do I solve a proportion?

Cross-multiply, then divide. For 7/12 = x/96, multiply 7 by 96 to get 672, then divide by 12 to get x = 56. The calculator shows each of those lines in the working panel.

Why does cross-multiplication work?

Because multiplying both sides of an equation by the same thing keeps it true. Multiplying 7/12 = x/96 by 12 and by 96 clears both denominators in one move and leaves 7 × 96 = 12 × x, which is an ordinary equation with one unknown.

What is the difference between a proportion and a ratio?

A ratio compares two quantities, such as 7 : 12. A proportion is the statement that two ratios are equal, such as 7/12 = 56/96. The ratio calculator handles the same maths in colon notation if that is how your problem is written.

Can a proportion have no answer?

Only when solving would mean dividing by zero. In 7/12 = x/0 there is no value of x that works, because nothing can be divided by zero. The calculator says so rather than showing a number.

What is the scale factor?

It is how many times bigger the second ratio is than the first: 56/7 gives a factor of 8, and 96/12 gives the same 8. Equal scale factors on both sides are the whole reason a proportion holds.

What is the difference between direct and inverse proportion?

In direct proportion, doubling one quantity doubles the other, and the ratio between them stays fixed — that is what this calculator solves. In inverse proportion, doubling one halves the other, so it is the product that stays fixed rather than the ratio.