Proportion Calculator FAQ
What is a proportion calculator?
A proportion calculator solves equations of the form a/b = c/d (direct proportion) or a × b = c × d (inverse proportion). Enter any three known values and the calculator finds the missing fourth using cross multiplication.
How do you solve a proportion with cross multiplication?
Cross multiply and divide. For 3/4 = x/8: multiply diagonally → 3 × 8 = 4 × x → 24 = 4x → x = 6. Another example: 5/x = 2/10 → 5 × 10 = 2 × x → x = 25. Cross multiplication works because if a/b = c/d, then ad = bc.
What is the rule of three?
The rule of three is a direct proportion method: if A → B, then C → x. Solve as x = B × C / A. Example: if 5 kg costs $15, how much do 8 kg cost? x = 15 × 8 / 5 = $24. For inverse proportion (more of one → less of the other): x = A × B / C.
What is the difference between direct and inverse proportion?
Direct proportion: both values increase or decrease together at the same rate. a/b = c/d. Example: more km driven → more fuel used. Inverse proportion: one value increases while the other decreases — their product stays constant. a × b = c × d. Example: more workers → fewer days to finish.
How do you scale a recipe with proportion?
Set up a direct proportion. Original recipe serves 4 and needs 200 g flour. You want to serve 6. Proportion: 200/4 = x/6 → x = 200 × 6 / 4 = 300 g flour. Apply the same ratio to every ingredient. The proportion calculator does this automatically for any quantity.
How do you use proportion for unit conversions?
Use a known equivalence as the ratio. Convert 75 miles to km: 1 mile = 1.609 km → 1/1.609 = 75/x → x = 75 × 1.609 = 120.7 km. Currency: $1 = €0.92, how many euros is $350? 1/0.92 = 350/x → x = €322. Any fixed ratio can serve as the proportion base.
How do you solve a work–time inverse proportion problem?
If 4 workers complete a job in 6 days, how long will 3 workers take? More workers = fewer days → inverse proportion: 4 × 6 = 3 × x → x = 24/3 = 8 days. Another example: a pump fills a tank in 5 hours; two identical pumps fill it in 5 × 1/2 = 2.5 hours.
What are common mistakes when solving proportions?
The most common error is mixing up direct and inverse proportion. Check: do the quantities move in the same direction (direct) or opposite directions (inverse)? Also verify the units match on each side of the ratio. Writing 3/4 = 8/x instead of 3/4 = x/8 swaps the unknown and gives a wrong answer.
Example
For a direct proportion, if 3 / 6 = x / 10, then cross multiplication gives 3 × 10 = 6 × x, so x = 5.
For an inverse proportion, if 4 × 12 = x × 8, then x = (4 × 12) / 8 = 6. This is the kind of setup used when more of one factor means less of the other.
