Fill three boxes, leave one blank. The tool solves the missing value in a proportion and shows the cross product check.
You get a wrong answer when you set up the ratio wrong.
Cross multiplication solves a proportion. A proportion means two fractions represent the same rate. If you mix units or swap rows, the equation stays solvable, but the result stops matching your situation.
A clean setup looks like this. Keep like things on the same row. If the left fraction is cups per people, the right fraction must stay cups per people.
In a proportion \( \frac{A}{B} = \frac{C}{D} \), the cross products match.
\( A \times D = B \times C \)
Once you know three numbers, you isolate the missing one with a single division.
This is the fastest way to break a correct setup.
If you start with distance over time on the left, keep distance over time on the right. Do not switch to time over distance half way through. If you want the inverse rate, rewrite both sides before you solve.
Suppose you have 3 items for 4 people. You want the matching number of items for 12 people.
Write items over people.
\( \frac{3}{4} = \frac{X}{12} \)
Cross products. \( 3 \times 12 = 4 \times X \). Then \( X = 36 / 4 = 9 \).
Quick check. 3 per 4 is 0.75. 9 per 12 is 0.75.
You have a recipe for 8 servings that uses 250 g of rice. You need 12 servings.
\( \frac{250}{8} = \frac{X}{12} \Rightarrow X = 375 \)
1 cm represents 5 km. Your measured distance is 3.4 cm.
\( \frac{1}{5} = \frac{3.4}{X} \Rightarrow X = 17 \)
A machine fills 18 bottles in 6 minutes. You want the count for 15 minutes.
\( \frac{18}{6} = \frac{X}{15} \Rightarrow X = 45 \)
This tool assumes the relationship is proportional across both fractions.
If the rate changes with scale, the answer misleads you. Example. Bulk discounts, progressive tax rates, non linear growth, or speed changes with traffic.
Also watch for zeros in denominators. A fraction with 0 in the bottom has no value, so the equation breaks.
If you see a direct proportion, the Single Rule of Three Direct is often the same math written in a story format.
If the relationship is inverse, use the Single Rule of Three Inverse. The setup changes, so cross multiplication only works after you place the right quantities across from each other.
For quick mental checks, compute the unit rate. Example. 18 bottles in 6 minutes is 3 bottles per minute. Then 15 minutes is 45 bottles.
If you solve proportions often, the tool saves keystrokes and reduces arithmetic slips.
If you are learning, do one problem by hand first. Then use the tool to verify your steps. For practice, pair this page with the Proportional Calculator to compare setups.
The tool uses the cross product identity \( A \times D = B \times C \). Then it solves the single variable equation by dividing both sides by the coefficient of the unknown.
Numbers are treated as decimals. The check repeats the cross product with the solved value and prints both products.
The tool prints decimals and rounds for display. Small rounding differences can appear in the cross product check when you input long decimals.
If you need an exact fraction result, rewrite the inputs as fractions before you solve, or keep more decimal places in your own work.
Cross multiplication is the same as clearing denominators.
Start with \( \frac{A}{B} = \frac{C}{D} \). Multiply both sides by \( B \times D \). You get \( A \times D = B \times C \).
This detail matters when you learn algebra. You are not using a trick. You are multiplying both sides by the same non zero value.
If the relationship is not proportional, do not force it into a proportion.
Example. A taxi fare with a base fee plus a per mile fee. The rate changes at the start. A single proportion cannot model it.
Example. Currency exchange with a fee. Convert, then subtract fee, or compute the fee separately. Do not hide it inside the ratio.
Reviewed on Mar 18, 2026.
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