OneTaskBy Tim King · Updated
Proportion Calculator
Cross Multiplication to Solve a/b = c/d for x, or Check a True Proportion
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How the Proportion Calculator works
This proportion calculator solves a/b = c/d when one of the four numbers is missing. Leave that box empty and it finds x by cross multiplication, showing each step. Fill in all four and it tells you whether the two ratios are equal, with the cross products that prove it.
A proportion says two ratios are equal: 3 is to 4 as 12 is to 16. Recipes, map scales, unit prices, fuel use and medicine doses all scale this way, so one known pair and one half of a new pair are enough to find the missing number.
How the proportion calculator solves for x
The formula comes from multiplying both sides of a/b = c/d by b and d, which gives a × d = b × c. These are the cross products, the numbers on each diagonal. Whichever value is missing, multiply the two known numbers on the full diagonal, then divide by the number sitting on the diagonal with x.
First example. 3/4 = 12/x. Cross multiply: 3 × x = 4 × 12 = 48, so x = 48 ÷ 3 = 16.
Second example. A recipe uses 250 g of flour for 4 people. For 6 people, 250/4 = x/6, so 4 × x = 250 × 6 = 1,500 and x = 375 g.
How many litres of paint cover 60 m² if 2 litres cover 25 m²? 2/25 = x/60, so 25 × x = 120 and x = 4.8 litres.
Everyday proportions solved by cross multiplication
| Problem | Proportion | Answer |
|---|---|---|
| Recipe: 3 eggs for 12 cakes, how many for 20? | 3/12 = x/20 | 5 |
| Map: 1 cm is 50 km, how far is 7.5 cm? | 1/50 = 7.5/x | 375 |
| Speed: 120 miles in 2 hours, how far in 5? | 120/2 = x/5 | 300 |
| Paint: 2 litres covers 25 m², how much for 60 m²? | 2/25 = x/60 | 4.8 |
| Price: 4 kg cost 10, what do 7 kg cost? | 4/10 = 7/x | 17.5 |
| Fuel: 30 litres for 400 km, how much for 650 km? | 30/400 = x/650 | 48.75 |
| Typing: 180 words in 3 minutes, how many in 10? | 180/3 = x/10 | 600 |
| Scale model 1:24, real car 4.2 m | 1/24 = x/4.2 | 0.175 |
| Concrete: 1 bag per 0.01 m³, bags for 0.45 m³ | 1/0.01 = x/0.45 | 45 |
| Wages: 150 for 8 hours, pay for 30 hours | 150/8 = x/30 | 562.5 |
| Dosage: 5 ml per 10 kg, dose for 34 kg | 5/10 = x/34 | 17 |
| Exchange: 1 unit buys 1.27, how many buy 500? | 1/1.27 = x/500 | 393.700787 |
| Knitting: 22 stitches = 10 cm, stitches for 48 cm | 22/10 = x/48 | 105.6 |
| Shadow: 2 m post casts 3 m, tree casts 18 m | 2/3 = x/18 | 12 |
| Mortar: 1 part cement to 4 sand, sand for 12 cement | 1/4 = 12/x | 48 |
| Reading: 40 pages in 1.5 hours, time for 300 | 40/1.5 = 300/x | 11.25 |
| Recipe: 250 g flour for 4, flour for 6 | 250/4 = x/6 | 375 |
| Water: 8 glasses = 2 litres, glasses in 3.5 litres | 8/2 = x/3.5 | 14 |
| Ratio 3:4 scaled so the second part is 28 | 3/4 = x/28 | 21 |
| Ratio 5:8 scaled so the first part is 45 | 5/8 = 45/x | 72 |
| Print: 6 pages per minute, minutes for 87 pages | 6/1 = 87/x | 14.5 |
| Seeds: 3 g per m², grams for 140 m² | 3/1 = x/140 | 420 |
Tips
- Keep units in the same places. If litres are on top on the left, litres go on top on the right.
- Check with the ratio. Each top divided by its bottom should give the same decimal.
- Not everything is proportional. Workers and time to finish a job go the other way, so cross multiplication gives the wrong answer.
FAQ
How do you solve a proportion?
Cross multiply and divide. Multiply the two numbers on the diagonal that has no unknown, then divide by the number on the same diagonal as x. For 5/8 = x/40 that is 5 × 40 = 200, and 200 ÷ 8 = 25. The calculator does the same steps whichever box you leave blank.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 3:4. A proportion is a statement that two ratios are equal, such as 3:4 = 12:16. The ratio calculator simplifies and splits single ratios, while this proportion calculator works with a pair of them and finds the missing term.
How do I check if two ratios are proportional?
Enter all four numbers. If the cross products a × d and b × c match, the ratios are proportional. 3/4 and 6/8 both give 24, so they are; 3/4 and 6/9 give 27 and 24, so they are not. Dividing each top by its bottom gives the same check as two decimals.
What is inverse proportion?
In inverse proportion one quantity goes up as the other goes down, so their product stays the same. If 4 painters take 6 days, 8 painters take 3 days, because 4 × 6 = 8 × 3. Cross multiplication does not apply here; multiply the known pair, then divide by the new value.
See also: all Algebra and Geometry tools, Arithmetic, Number Theory, Statistics, Trigonometry and Calculus.
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