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Solving proportions with fractions and mixed numbers

Keep exact answers, simplify at the end, and avoid early rounding.

Fractional inputs do not change the logic of a proportion. They change the arithmetic inside each step. A fraction such as 3/4 can be a single entry in a larger ratio, so take care to distinguish a value from the bar dividing the two values.

A fraction inside a proportion

Suppose (1/2)/3 = x/9. Cross multiplication gives (1/2) × 9 = 3x. The left side is 9/2. Dividing by 3 gives x = (9/2) × (1/3) = 9/6 = 3/2.

Check by dividing each top entry by its bottom entry. Both ratios equal 1/6. Writing parentheses around fractional entries prevents the slash notation from becoming ambiguous.

Convert mixed numbers first

A mixed number 1 1/2 means 1 + 1/2 = 3/2. In general, multiply the whole part by the denominator and add the numerator. The input fields accept mixed numbers with a space, such as 1 1/2. For a negative mixed number, -1 1/2 means -(1 + 1/2), or -3/2.

Example: (1 1/2)/4 = x/8. The denominator doubles from 4 to 8, so the numerator doubles too: (3/2) × 2 = 3. This is an easy place to use the scale-factor method rather than longer multiplication.

Dividing by a fraction

To divide by a nonzero fraction, multiply by its reciprocal. For 3/4 = (1/2)/x, cross multiplication gives 3x = 4 × (1/2) = 2, hence x = 2/3. If you instead start with the general formula, you get x = (4 × 1/2)/3, the same value.

Why exact arithmetic helps

Rounding 1/3 to 0.33 before calculating can shift the final result. Keep 1/3 as a fraction through the calculation and round only if the question requests a decimal. This calculator shows the simplified exact fraction first; a decimal with up to eight decimal places is a convenience, not a replacement for the exact value.

A fraction with denominator zero is never a valid input. For decimal formatting, read proportions with decimals. If the layout is the confusing part, start with the four-position formula table.