Ratio & Proportion Calculator (Solve for x)
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A ratio and proportion calculator finds the missing term when two ratios are equal. For 5/8 = x/24, cross-multiply: 8 × x = 5 × 24 = 120, so x = 120 ÷ 8 = 15, and 5:8 = 15:24. The same tool simplifies ratios (12:18 = 2:3), divides an amount in a ratio and turns a ratio into fractions and percents.
In the proportion 5 : 8 = x : 24, x = 15, so 5 : 8 = 15 : 24.
Both bars split in the same proportion: green is about 38.5% of each bar. That is what makes the ratios equal.
Show steps
- Write the proportion as two equal fractions: 5/8 = x/24.
- Cross-multiply. The product of the outer terms equals the product of the inner terms (A × D = B × C): 5 × 24 = 8 × x.
- Simplify: 8x = 120.
- Divide both sides by 8: x = 120 ÷ 8 = 15.
- Shortcut with a scale factor: 24 ÷ 8 = 3, so the second ratio is the first one × 3: x = 5 × 3 = 15.
- Check: 5 ÷ 8 = 0.625 and 15 ÷ 24 = 0.625. The two ratios are equal.
Keep the units in the same order on both sides: if the first ratio is mg : mL, the second must be mg : mL too.
How to use the ratio and proportion calculator
- Solve proportion: fill in three of the four boxes in A : B = C : D and type x (or leave blank) in the fourth. Fill all four to check whether the ratios are proportional.
- Simplify ratio: type a ratio with colons, such as 12:18, 6:9:15 or 1.5:2.25.
- Divide an amount: enter a total and a ratio, such as 60 and 2:3:5, to get each share.
- Ratio to fraction & %: enter a ratio to see each part as a fraction and a percent of the whole.
- Open Show steps to see the full working, and use Copy result to paste the answer into your notes.
What ratios and proportions are
A ratio compares two or more quantities: 3:4 means “3 for every 4”. It can be written as 3:4, 3 to 4 or 3/4. A proportion is an equation stating that two ratios are equal, such as 3/4 = 9/12. Both ratios simplify to the same thing, so they describe the same relationship at different sizes.
Cross-multiplication: the proportion formula
For a proportion a/b = c/d (with b and d not zero), the cross products are equal:
a × d = b × c
Rearrange it for whichever term is missing:
| Missing term | Formula | Example |
|---|---|---|
| a | a = b × c ÷ d | x/7 = 4.5/3 gives x = 7 × 4.5 ÷ 3 = 10.5 |
| b | b = a × d ÷ c | 3/x = 5/7 gives x = 3 × 7 ÷ 5 = 4.2 |
| c | c = a × d ÷ b | 5/8 = x/24 gives x = 5 × 24 ÷ 8 = 15 |
| d | d = b × c ÷ a | 2/3 = 8/x gives x = 3 × 8 ÷ 2 = 12 |
A faster mental route is the scale factor. In 5/8 = x/24, the denominator went from 8 to 24, which is × 3, so the numerator must also be × 3: x = 15. Cross-multiplication always works, even when the scale factor is not a whole number.
How to simplify a ratio
- If any term is a decimal or fraction, multiply every term by the same number to make them all whole. 1.5:2.25 × 4 = 6:9.
- Find the greatest common factor (GCF) of all the terms.
- Divide every term by the GCF. 6:9 ÷ 3 = 2:3.
Three-part ratios work the same way: 6:9:15 has GCF 3, so it simplifies to 2:3:5.
How to divide an amount in a ratio
To share $60 in the ratio 2:3:5, add the parts: 2 + 3 + 5 = 10. One part is $60 ÷ 10 = $6. The shares are 2 × 6 = $12, 3 × 6 = $18 and 5 × 6 = $30, and they add back to $60.
Ratio to fraction and percent
A ratio a:b gives two kinds of fractions. Part to whole: a/(a + b). In 3:5 there are 8 parts, so the first part is 3/8 = 37.5% of the whole and the second is 5/8 = 62.5%. Part to part: a/b. Here 3/5 = 0.6, so the first amount is 60% of the second. Questions about “what fraction of the total” need the part-to-whole form.
Worked examples
Recipe: scaling up
A recipe uses 3 cups of flour for 4 cups of milk. How much flour goes with 12 cups of milk? Set up flour : milk = flour : milk: 3/4 = x/12. Cross-multiply: 4x = 36, so x = 9 cups of flour.
Shopping: price per item
3 notebooks cost $4.50. What do 7 cost? 3/4.50 = 7/x, so 3x = 31.50 and x = $10.50. The unit price is $1.50 per notebook.
Medication dose (nursing)
A liquid has 250 mg in 5 mL and the order is 400 mg. Write mg : mL = mg : mL: 250/5 = 400/x. Cross-multiply: 250x = 2,000, so x = 8 mL. This is a textbook practice example. Real doses must always be checked against the order and your clinical guidance.
Common ratio and proportion mistakes
| Mistake | Example | Fix |
|---|---|---|
| Mixing the order of units | mg/mL = mL/mg | Keep the same order on both sides |
| Using part to part when part to whole is asked | 3:5 read as 3/5 of the total | Divide by the total parts: 3/8 |
| Adding instead of multiplying | 2:3 = 8:9 (added 6) | Scale both terms by the same factor: 8:12 |
| Stopping before fully simplified | 24:36 = 12:18 | Divide by the GCF, 12: 2:3 |
| Rounding too early | Rounding one part before scaling | Keep exact fractions until the last step |
Ratios and proportions practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Cross-multiply: 9x = 4 × 27 = 108, so x = 12. Adding 18 to 4 (to get 22) is the common slip.
The GCF of 45 and 60 is 15, so 45:60 = 3:4. 9:12 and 15:20 are equivalent but not fully simplified.
3 + 4 = 7 parts, one part is 84 ÷ 7 = $12, so the shares are $36 and $48.
There are 2 + 3 = 5 parts and 2 of them are boys, so 2/5. 2/3 compares boys to girls, not boys to the class.
Cross products: 6 × 20 = 120 and 8 × 15 = 120. They match, and both ratios simplify to 3:4.
7 + 13 = 20 parts, and 7/20 = 0.35 = 35%. 53.8% is 7/13, the part-to-part comparison.
1 + 2 + 3 = 6 parts, one part is 15, and the middle term is 2 parts: 30.
Quiz complete
Frequently asked questions
What is ratio and proportion?
A ratio compares quantities, such as 3 boys for every 4 girls (3:4). A proportion says two ratios are equal, such as 3:4 = 9:12. If a class has that ratio and 12 girls, it has 9 boys.
What is the ratio and proportion formula?
For a/b = c/d, the cross products are equal: a × d = b × c. To solve 5/8 = x/24, write 8x = 120, so x = 15. Check by dividing: 5 ÷ 8 = 0.625 and 15 ÷ 24 = 0.625.
How do you do ratio and proportion word problems?
Write the two ratios with the same units in the same order, put x where the unknown goes, and cross-multiply. "3 notebooks cost $4.50, how much for 7?" becomes 3/4.50 = 7/x, so x = $10.50.
How do you find the proportion of each part in a ratio?
Divide each term by the total of the terms. In 3:5 the total is 8, so the parts are 3/8 = 37.5% and 5/8 = 62.5%. With 40 beads in that ratio, there are 15 red and 25 blue.
What is the ratio and proportion method in nursing?
Nurses set up have : have = want : x with matching units, for example 250 mg : 5 mL = 400 mg : x mL, which gives x = 8 mL. Always follow your program's or facility's dosage rules.
How do you work with a ratio of three numbers?
Treat it like a two-term ratio. To simplify, divide all three terms by their GCF. To share an amount, add the parts and find the value of one part: $60 in 2:3:5 is $12, $18 and $30.
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