Ratios & Proportions Calculator

Simplify, compare, and solve ratios and proportions with ease

Simplify Ratio
Equivalent Ratios
Solve Proportion
Compare Ratios
Scale Ratio

Simplify Ratio

Reduce a ratio to its simplest form

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Find Equivalent Ratios

Generate equivalent ratios by multiplying or dividing

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Solve Proportion

Find the missing value in a proportion (use 'x' for unknown)

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💡 Example Problems:
  • If 3:4 = 6:x, find x (Answer: x = 8)
  • If x:5 = 12:15, find x (Answer: x = 4)
  • If 2:x = 8:20, find x (Answer: x = 5)

Compare Ratios

Determine which ratio is greater

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Scale Ratio

Scale a ratio up or down by a factor

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📖 How to Use This Calculator

  • Simplify Ratio: Reduce any ratio to its simplest form (e.g., 6:8 → 3:4)
  • Equivalent Ratios: Find multiple ratios equal to your original ratio
  • Solve Proportion: Find the unknown value (x) in a proportion equation
  • Compare Ratios: Determine which of two ratios represents a larger value
  • Scale Ratio: Multiply all terms by a scale factor
  • Supports decimal numbers and multiple terms (for simplification)
  • Visual representations help understand ratio relationships

Ratios & Proportions Made Easy

A complete guide to understanding ratios, writing equivalent ratios, and solving proportions – packed with formulas, real‑life examples & practice questions.

What is a ratio?

A ratio compares two (or more) quantities showing how many times one value contains another. Ratios can be written with a colon (3 : 2), as a fraction (32), or using the word “to” (3 to 2).

How to simplify a ratio

Divide each term by their greatest common divisor (GCD).

Example – Simplify 18 : 24.

GCD(18, 24) = 6 → 18 ÷ 6 : 24 ÷ 6 = 3 : 4.

Finding equivalent ratios

Multiply or divide each term of a ratio by the same non‑zero number.

Example: 3 : 4 is equivalent to 6 : 8 (×2) or 9 : 12 (×3).

What is a proportion?

A proportion is an equation stating that two ratios are equal. For instance, ab = cd or a : b = c : d.

How to solve proportions

  • Cross‑multiplication – set products equal: if ab = cd, then a × d = b × c.
  • Scaling – identify a factor that links known terms.

Example – Solve 7/x = 14/20.

Cross‑multiply: 7 × 20 = 14 × x → 140 = 14x → x = 10.

Quick‑fire examples

Example 1 – Recipe ratio

A drink mix calls for water and syrup in a 5 : 1 ratio. If you have 750 ml water, how much syrup is needed?

Solution: 5 parts → 750 ml, so 1 part = 150 ml. Syrup = 150 ml.

Example 2 – Map scale

A map scale is 1 : 50,000. If two towns are 8 cm apart on the map, what’s the real‑world distance?

Solution: 8 cm × 50,000 = 400,000 cm = 4 km.

Practice questions

Try these. Click to reveal answers.

1. Simplify 45 : 60.

Divide by 15 → 3 : 4.

2. If 4 pens cost AED 18, what is the cost of 10 pens at the same rate?

Set 4/18 = 10/x → 4x = 180 → x = AED 45.

3. In a class, the ratio of boys to girls is 7 : 9. If there are 56 boys, how many girls?

Scaling factor 7→56 (×8). Girls = 9 × 8 = 72.

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Master Ratios & Proportions

Frequently Asked Questions

What’s the difference between a ratio and a fraction?

A ratio compares two quantities; a fraction represents a part of a single quantity. Ratios can compare more than two values (e.g., 2 : 3 : 5) whereas fractions typically involve two values (numerator/denominator).

How can I check if two ratios form a proportion?

Cross‑multiply the terms. If the products are equal, the ratios are proportional (e.g., for a/b = c/d, check if a×d = b×c).

Do ratios need to be in simplest form?

Simplifying makes ratios easier to interpret and compare, but it’s not always strictly required unless specified by the problem or context. Often, ratios are presented in simplest form for clarity.

What is a ratio?

A ratio compares two or more quantities, indicating their relative sizes or how many times one value contains another. Ratios can be written with a colon (e.g., 3:2), as a fraction (e.g., 32), or using the word "to" (e.g., 3 to 2).

What is a proportion?

A proportion is an equation that states that two ratios are equal. For example, ab = cd or a : b = c : d.

What is the difference between a ratio and a proportion?

A **ratio** is a comparison of two or more numbers (e.g., 1:2). A **proportion** is an equation that declares two ratios to be equivalent (e.g., 1:2 = 2:4). They are not the same thing, but a proportion is built from two equal ratios.

How do you solve ratios and proportions?

To solve for an unknown in a proportion, the most common method is **cross-multiplication**. If you have ab = cd, then you can set the products equal: a × d = b × c. You can also use **scaling** by finding the multiplication or division factor between corresponding known terms.

How do you solve for an unknown (e.g., 'x') in a proportion?

If you have a proportion like 7x = 1420, you can cross-multiply: 7 × 20 = 14 × x. This simplifies to 140 = 14x. Then, divide both sides by 14 to find x: x = 10.

How to simplify a ratio?

To simplify a ratio, divide all terms in the ratio by their Greatest Common Divisor (GCD). For example, to simplify 18:24, the GCD of 18 and 24 is 6. Dividing both terms by 6 gives the simplified ratio 3:4.

How to find equivalent ratios?

To find equivalent ratios, multiply or divide all terms in the ratio by the same non-zero number. For example, 3:4 is equivalent to 6:8 (multiplying both by 2) or 9:12 (multiplying both by 3).

How can I check if two ratios form a proportion?

Set them up as a proportion (e.g., ab = cd) and then perform cross-multiplication. If the products (a × d and b × c) are equal, then the ratios form a proportion.

Example: Are the ratios 25:45 and 15:27 proportional?

Set up as fractions: 2545 and 1527. Cross-multiply: 25 × 27 = 675. And 45 × 15 = 675. Since the products are equal (675 = 675), the ratios are proportional.

Why are ratios and proportions important, and how are they used in everyday life?

Ratios and proportions are crucial for comparing quantities and scaling. They are used daily in:

  • **Cooking:** Adjusting recipes (e.g., doubling for more servings).
  • **Maps and Blueprints:** Understanding scale (e.g., 1 cm = 100 meters).
  • **Finance:** Calculating interest rates, converting currencies.
  • **Healthcare:** Determining medication dosages.
  • **Science & Engineering:** Mixing solutions, designing structures.
They help us solve for unknown values based on known relationships.

What is the difference between a rate, a ratio, and a proportion?

  • **Ratio:** Compares two quantities of the *same type* (e.g., 3 apples to 2 oranges).
  • **Rate:** Compares two quantities with *different units* (e.g., 60 miles per hour, 10 dollars per kilogram). Rates often imply change or movement.
  • **Proportion:** An equation stating that two ratios or two rates are equal (e.g., 3:2 = 6:4, or 60 miles/hour = 120 miles/2 hours).

How to approach ratio and proportion word problems?

  1. **Identify Quantities:** Determine what quantities are being compared.
  2. **Set up the Ratio:** Write the given ratio clearly.
  3. **Form the Proportion:** Use the given information and an unknown variable (like 'x') to set up an equation with two equal ratios. Make sure corresponding quantities are in the same position in both ratios.
  4. **Solve:** Use cross-multiplication or scaling to solve for the unknown variable.
  5. **Check:** Ensure your answer makes sense in the context of the problem.

Do ratios need to be in simplest form?

While not strictly required unless specified, simplifying ratios makes them much easier to interpret and compare. It's generally good practice to present ratios in their simplest form.