Simplify ratios, find missing values, check if ratios are proportional, and scale recipes, maps, and measurements.
To simplify a ratio, divide every part by their greatest common factor (GCF). For example, 8:12 has a GCF of 4, so it simplifies to 2:3. A ratio compares two or more quantities, showing how much of one there is compared to another. This ratio calculator simplifies ratios, finds equivalent ratios, scales quantities and solves proportions — each with clear steps.
a : b = c : d — leave one blank
| Form | Value |
|---|
A ratio compares two or more quantities, showing how much of one there is relative to another. It is written with a colon, like 3:2, and read as "three to two." Ratios are closely linked to fractions, proportions and percentages — they are all ways of comparing numbers. A ratio can be part-to-part (comparing two groups) or part-to-whole (comparing one group to the total).
To simplify a ratio, you divide each part by the greatest common factor (GCF). To scale a ratio, you multiply each part by the same number. To solve a proportion, you cross-multiply.
These tables clarify how ratios relate to fractions, proportions and different ratio types.
| Concept | What It Means | Example |
|---|---|---|
| Ratio | Compares quantities | 3:2 |
| Fraction | Part of a whole | 3/5 |
| Proportion | Two equal ratios | 3:2 = 6:4 |
| Percentage | Part per hundred | 60% |
| Ratio Type | Compares | Example (3 boys, 2 girls) |
|---|---|---|
| Part-to-part | One group to another | Boys to girls = 3:2 |
| Part-to-whole | One group to the total | Boys to all = 3:5 |
| Ratio | Simplified | GCF Used |
|---|---|---|
| 10:15 | 2:3 | 5 |
| 12:16 | 3:4 | 4 |
| 9:27 | 1:3 | 9 |
| 25:100 | 1:4 | 25 |
| Application | Given | Find | Calculation |
|---|---|---|---|
| Recipe scaling | Recipe for 4: 2 cups flour. Scale to 10. | Flour needed | 2/4 = x/10 → x = 5 cups |
| Map distance | Scale 1:50,000. Map distance 3cm. | Real distance | 3 × 50,000 = 150,000 cm = 1.5 km |
| Concrete mix | Cement:sand:gravel = 1:2:3 | Parts per 12 bags total | 2 cement, 4 sand, 6 gravel |
| Sharing profit | Partners share 3:5 | Each share of $24,000 | 3/8 × $24k = $9k; 5/8 × $24k = $15k |
divide each part by the GCFmultiply each part by the same numberx = (b × c) ÷ across-multiply — equal products matcha:b → a/(a+b) part-to-whole(part ÷ total) × 100
1) 2:3 2) 1:2 3) e.g. 4:6 4) 4:8 = 1:2 5) 1/5
1) 5 × 24 ÷ 8 = 15, so x = 15 2) 45:60 = 3:4 (GCF 15) 3) 3:2 → 9:6, so 6 cups sugar 4) 6×15 = 90 and 9×10 = 90, equal → yes 5) total parts 5 → $100÷5 = $20; shares $60 and $40
What is a ratio?
A ratio compares two or more quantities, showing how much of one there is relative to another. It is written with a colon, such as 3:2, and read "three to two." Ratios can compare part-to-part (one group to another) or part-to-whole (one group to the total).
How do you simplify a ratio?
Divide every part of the ratio by their greatest common factor (GCF). For example, 8:12 has a GCF of 4, so dividing both parts gives 2:3. A ratio is in its simplest form when the parts share no common factor other than 1. The calculator does this and shows the steps.
How do you calculate ratios?
Decide what you are comparing, write the quantities in order separated by a colon, then simplify by dividing by the GCF. To scale a ratio, multiply each part by the same number. To solve a proportion, cross-multiply. Enter your numbers in the calculator to see each step.
What is the difference between a ratio and a fraction?
A ratio compares quantities to each other, like 3:2, while a fraction shows a part of a whole, like 3/5. They are related: a part-to-whole ratio can be written as a fraction. In 3:2, the first group is 3/5 of the total, since the whole is 3 + 2 = 5 parts.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 3:2. A proportion is a statement that two ratios are equal, such as 3:2 = 6:4. You use proportions to solve for an unknown value by cross-multiplying, which is how the calculator finds a missing term.
How do you find equivalent ratios?
Multiply or divide each part of the ratio by the same number. For example, 3:5 becomes 6:10 when multiplied by 2, or 12:20 when multiplied by 4. All of these describe the same relationship. To check if two ratios are equivalent, cross-multiply and compare the products.
How do you convert a ratio to a fraction or percentage?
For a part-to-whole fraction, put one part over the total of all parts — in 3:2 the first part is 3/5. To get a percentage, divide the part by the total and multiply by 100, so 3:2 gives 60% and 40%. This links ratios to fractions and percentages.
What is a unit ratio?
A unit ratio has 1 as one of its terms, such as 1:4 or 5:1. It shows how many of one quantity correspond to a single unit of another, which makes comparisons easy. Unit ratios are closely related to unit rates, like kilometres per litre or price per item.
What is a part-to-part ratio?
A part-to-part ratio compares one group directly with another. If a class has 3 boys and 2 girls, the part-to-part ratio of boys to girls is 3:2. It does not include the total — it only compares the two groups with each other.
What is a part-to-whole ratio?
A part-to-whole ratio compares one group with the total. With 3 boys and 2 girls, the whole class is 5, so the part-to-whole ratio of boys to the class is 3:5. Part-to-whole ratios convert neatly into fractions and percentages.
How do you scale a recipe using ratios?
Keep the ratio the same and multiply each ingredient by the same factor. If a recipe uses flour and sugar in a 2:1 ratio and you want to double it, multiply both amounts by 2. The ratio stays 2:1, but the quantities double, so the taste stays balanced.
Does this ratio calculator show the steps?
Yes. It simplifies ratios, finds equivalent ratios, scales quantities and solves proportions, showing the working at each stage — including the greatest common factor used to simplify. That makes it useful for checking homework and learning the method, not just getting an answer.