Ratio Calculator

Simplify ratios and find equivalent ratios with step-by-step solutions

Simplify a Ratio

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Find Missing Value in Ratio

If A : B = C : D, find the missing value

: = :

Understanding Ratios

A ratio is a comparison of two or more quantities. It shows how many times one quantity contains another. Ratios can be written in three ways:

  • Using a colon: 3:4
  • Using the word "to": 3 to 4
  • As a fraction: 3/4

Simplifying Ratios

To simplify a ratio, divide all parts by their greatest common divisor (GCD).

Example: 12:18

GCD(12, 18) = 6

12:18 = (12/6):(18/6) = 2:3

Solving Proportions

A proportion states that two ratios are equal. To find a missing value:

If A:B = C:D, then D = (B × C) / A

This is called cross multiplication

Real-World Applications

  • Cooking: Mix ingredients in specific ratios
  • Finance: Compare prices or investment returns
  • Construction: Mix concrete, mortar, or other materials
  • Maps: Scale ratios on maps and models

Examples

Example 1: Simplify 24:36
Problem: Simplify 24:36
Step 1: Find the GCD of 24 and 36
    24 = 2^3 × 3
    36 = 2^2 × 3^2
    GCD = 2^2 × 3 = 12
Step 2: Divide both by GCD
    24/12 = 2, 36/12 = 3
Result: 24:36 = 2:3
Example 2: Solve 3:4 = 15:x
Problem: Find x where 3:4 = 15:x
Step 1: Set up as proportion
    3/4 = 15/x
Step 2: Cross multiply
    3 × x = 4 × 15
    3x = 60
Step 3: Solve for x
    x = 60/3 = 20
Result: 3:4 = 15:20
Example 3: Simplify 45:60
Problem: Simplify 45:60
Step 1: Find the GCD
    45 = 3^2 × 5
    60 = 2^2 × 3 × 5
    Common factors: 3 × 5 = 15
Step 2: Divide both by GCD
    45/15 = 3, 60/15 = 4
Result: 45:60 = 3:4
Example 4: Solve for missing term
Problem: If 2:5 = 8:x, find x
Step 1: Cross multiply
    2 × x = 5 × 8
    2x = 40
Step 2: Solve for x
    x = 40/2 = 20
Result: 2:5 = 8:20
Example 5: Real-world ratio
Problem: A recipe calls for 3 cups flour to 2 cups sugar. How much sugar for 9 cups flour?
Step 1: Set up the ratio
    Flour:Sugar = 3:2
Step 2: Set up proportion with 9 cups flour
    3:2 = 9:x
Step 3: Solve
    3x = 18, x = 6
Result: You need 6 cups of sugar

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