Proportion Calculator
Solve for the unknown in any proportion — A/B = C/D.
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How to Solve Proportions
A proportion states that two ratios are equal: A/B = C/D. Proportions are used to scale recipes, convert units, calculate map distances, determine drug dosages, and solve many real-world problems.
Cross-Multiplication Method
To solve for an unknown, use cross-multiplication. If A/B = C/D and D is unknown: D = (B × C) / A. This works because multiplying both sides of the proportion by B × D gives: A × D = B × C, and dividing both sides by A gives D = (B × C) / A.
Example: 3/4 = 9/D → D = (4 × 9) / 3 = 36/3 = 12. Check: 3/4 = 9/12 = 0.75 ✓
Direct vs. Inverse Proportions
Direct proportion: as A increases, B increases proportionally (y = kx). Inverse proportion: as A increases, B decreases proportionally (y = k/x). This calculator solves direct proportions.
Real-World Applications
Recipe scaling: if a recipe for 4 servings needs 2 cups of flour, how much for 10 servings? 2/4 = x/10 → x = 5 cups. Map reading: if 1 inch represents 50 miles and a route measures 3.5 inches, the real distance is 175 miles.
Worked Example: Drug Dosage
A medication is dosed at 5 mg per kg of body weight. A patient weighs 68 kg. How many mg are needed? Set up the proportion: 5 mg / 1 kg = x mg / 68 kg. Cross-multiply: x = 5 × 68 = 340 mg.
If the medication comes in 250 mg tablets, the patient needs 340/250 = 1.36 tablets. In clinical settings, this would round to 1.5 tablets (cutting in half) or the next available dosage form.
Proportion Problem Examples
| Problem | Setup | Answer |
|---|---|---|
| Scale model: 1:50, model is 8 cm | 1/50 = 8/x | x = 400 cm (4 m) |
| Speed: 60 mph for how far in 2.5 hr? | 60/1 = x/2.5 | x = 150 miles |
| Recipe: 3 eggs for 12 cookies, need 30 | 3/12 = x/30 | x = 7.5 eggs |
| Tax: 8% on $45 purchase | 8/100 = x/45 | x = $3.60 |
Frequently Asked Questions
A proportion is an equation stating that two ratios are equal: A/B = C/D. Solving a proportion means finding the unknown value when three values are known.
Use cross-multiplication: A × D = B × C. Solve for the unknown by dividing. Example: 2/5 = x/20 → x = (2 × 20)/5 = 8.
Cross-multiply: 3 × 20 = 4 × x → 60 = 4x → x = 15.
A ratio compares two quantities (3:4). A proportion is an equation stating two ratios are equal (3/4 = 6/8). All proportions involve ratios, but not all ratios are proportions.
Yes, cross-multiplication works the same way. A negative result simply means the unknown is negative.
In an inverse proportion, as one value increases, the other decreases at the same rate: A × B = constant. For example, if 3 workers take 8 days to finish a job, how long would 6 workers take? 3 × 8 = 6 × d → d = 24/6 = 4 days. Inverse proportions are solved by multiplying rather than using A/B = C/D.
Similar triangles have equal corresponding angles, and their corresponding sides are proportional. If triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF. You can find an unknown side length by setting up a proportion with the known sides. This is the basis for calculating heights of buildings from shadow lengths and distances in navigation.