Ratio Calculator — Solve and Simplify Ratios
Solve ratio proportions (A:B = C:?) and simplify ratios to their lowest terms. See also Fraction Calculator and Percentage Calculator.
Solve Ratio: A : B = C : ?
Simplify a Ratio
How to Solve Ratio Problems
A ratio compares two quantities. When you have a proportion like A:B = C:D, if three values are known, you can find the fourth. The key principle is cross-multiplication: A × D = B × C. To find D, rearrange to D = (B × C) / A. This calculator also simplifies ratios by dividing both parts by their greatest common divisor (GCD).
Ratio Formula
Proportion: A : B = C : D
Cross multiply: A × D = B × C
Solve for D: D = (B × C) / A
Simplify ratio A : B:
Divide both by GCD(A, B)
Example
2 : 3 = 4 : ?
Cross multiply: 2 × ? = 3 × 4
2 × ? = 12
? = 12 / 2 = 6
So 2:3 = 4:6
Frequently Asked Questions
What is a ratio?
A ratio is a comparison of two quantities showing how many times one value contains or is contained within the other. For example, a ratio of 3:2 means for every 3 of the first quantity, there are 2 of the second.
What is a proportion?
A proportion is an equation stating that two ratios are equal. For example, 1:2 = 3:6 is a proportion because both ratios simplify to the same value (1:2). Proportions are solved using cross-multiplication.
How do you simplify a ratio?
Divide both numbers by their greatest common factor (GCF). For example, 15:25 → GCF(15,25) = 5 → 15÷5 : 25÷5 = 3:5.
Can ratios have decimals?
Yes, ratios can involve decimals. To simplify a decimal ratio like 1.5:2.5, multiply both by 10 to get 15:25, then simplify to 3:5. This calculator handles decimal inputs automatically.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (A:B), while a fraction represents a part of a whole (A/B). The ratio 3:4 means "3 to 4," while the fraction 3/4 means "3 out of 4." They are related but used in different contexts.
Solved Examples — Ratios
Example: A recipe uses flour and sugar in a 5:2 ratio. If you use 750g of flour, how much sugar do you need?
Solution:
Step 1: Set up proportion: 5:2 = 750:x
Step 2: Cross multiply: 5 × x = 2 × 750
Step 3: 5x = 1500
Step 4: x = 300g
Answer: 300g of sugar
Example: Simplify the ratio 84:126
Solution:
Step 1: Find GCF(84, 126) = 42
Step 2: 84 ÷ 42 = 2
Step 3: 126 ÷ 42 = 3
Answer: 2:3
Example: A map scale is 1:50,000. If two cities are 3.5 cm apart on the map, what is the actual distance?
Solution:
Step 1: 1 cm on map = 50,000 cm in reality
Step 2: 3.5 cm × 50,000 = 175,000 cm
Step 3: Convert: 175,000 cm = 1,750 m = 1.75 km
Answer: 1.75 km
Practice Questions
Try these on your own:
- Simplify the ratio 45:60 (Answer: 3:4)
- If 3:7 = x:28, find x (Answer: 12)
- A class has boys and girls in a 3:5 ratio. If there are 40 students total, how many are boys? (Answer: 15)
- Mix paint in ratio 2:3:5. If you need 500mL total, how much of each color? (Answer: 100:150:250 mL)
- Simplify 2.5:3.75 to a whole-number ratio (Answer: 2:3)
- If $240 is split in ratio 5:3, how much does each person get? (Answer: $150 and $90)
Common Mistakes to Avoid
The most common mistake with ratios is confusing the order — a ratio of 3:5 is NOT the same as 5:3. Always make sure which quantity goes first. Another error is adding ratio parts incorrectly when finding actual values: if a ratio is 2:3 and the total is 100, each "part" = 100 ÷ 5 = 20, so the amounts are 40 and 60 (not 2 and 3). Students also sometimes try to add or subtract ratios directly (like fractions), but ratios represent relationships, not quantities. When simplifying, make sure to divide BOTH parts by the same number. Also, be careful with three-part ratios: to find a missing value in A:B:C, you need to use the specific pair relationship, not all three at once.
Key Takeaways
- A ratio compares quantities. Order matters: 3:5 ≠ 5:3.
- Simplify by dividing both parts by their GCF: 12:18 → 2:3.
- To solve proportions (A:B = C:D), cross multiply: A×D = B×C.
- To divide a total using a ratio, add the parts, divide total by sum, then multiply each part.
- Ratios can be expressed as fractions (3:4 = 3/4) or percentages (3:4 = 43%:57%).
- Real-world uses: recipes, maps, mixing, financial splits, scale models, and unit conversions.