A proportion says two fractions are equal — a/b = c/d — and if you know any three of the four numbers involved, the fourth is always solvable. This shows up constantly in scaling recipes, converting measurements, and reading maps: “if 2 cups makes 3 servings, how many cups make 6 servings?” is exactly this kind of problem.
How to Solve for an Unknown Fraction Value (step by step)
Every version below starts from the same cross-multiplied equation: a × d = b × c. Which letter you solve for just depends on which one is missing.
Solve First Numerator (a)
Given b, c, and d, solve a/b = c/d for a.
a = (b × c) ÷ d
With b = 3, c = 4, d = 6:
a = (3 × 4) ÷ 6 = 2
2/3 = 4/6 ✓
Solve First Denominator (b)
Given a, c, and d, solve a/b = c/d for b.
b = (a × d) ÷ c
With a = 2, c = 4, d = 6:
b = (2 × 6) ÷ 4 = 3
2/3 = 4/6 ✓
Solve Second Numerator (c)
Given a, b, and d, solve a/b = c/d for c.
c = (d × a) ÷ b
With a = 2, b = 3, d = 6:
c = (6 × 2) ÷ 3 = 4
2/3 = 4/6 ✓
Solve Second Denominator (d)
Given a, b, and c, solve a/b = c/d for d.
d = (c × b) ÷ a
With a = 2, b = 3, c = 4:
d = (4 × 3) ÷ 2 = 6
2/3 = 4/6 ✓
What your results mean
Whichever value you solved for completes the proportion so both fractions are exactly equal. Because the underlying relationship is the same equation solved four different ways, plugging your answer back into the original fraction and cross-multiplying should always confirm both sides match — that’s a quick way to check your work by hand.
Results aren’t always whole numbers. If your three known values don’t divide evenly, the missing value will be a decimal — which is still the correct, exact answer, just not a “clean” one.
A real example: scaling a recipe
If 2 cups of flour makes 3 servings, how many cups make 6 servings? That’s the proportion 2/3 = c/6, solving for the second numerator:
c = (6 × 2) ÷ 3 = 4 cups
Where this comes up
Unit conversions, recipe scaling, map scales, and similar-triangle geometry problems are all proportions in disguise. If you already know all four fraction values and just want to check whether they’re truly proportional, use the comparing fractions calculator on the cross-multiplied pair instead. For generating a scaled-up version of a single known fraction, see the equivalent fractions calculator.