Ratio Calculator

How to Calculate Ratios

Ratios are a fundamental concept in mathematics, used to compare quantities and express relationships between numbers. Here's a comprehensive guide on how to work with ratios:

Ratio Formulas and Definitions

1. Ratio Definition:
   A ratio is a comparison of two or more quantities, typically expressed as a:b or a:b:c.
2. Ratio Value:
   \[ \text{Ratio Value} = \frac{a}{b} \] Where a and b are the terms of the ratio.
3. Reducing a Ratio:
   To reduce a ratio, divide both terms by their greatest common divisor (GCD). \[ \text{Reduced Ratio} = \frac{a \div \text{GCD}}{b \div \text{GCD}} \]
4. Comparing Ratios:
   Convert ratios to decimal form and compare the results. \[ \text{Ratio 1} = \frac{a_1}{b_1}, \quad \text{Ratio 2} = \frac{a_2}{b_2} \]
5. Scaling a Ratio:
   Multiply both terms of the ratio by the scale factor. \[ \text{Scaled Ratio} = (a \times \text{scale}) : (b \times \text{scale}) \]

Calculation Steps

Let's go through an example for each type of ratio calculation:

1. Calculate Ratio Value

Example: Find the ratio value of 3:4

1. Identify the terms: a = 3, b = 4
2. Apply the formula: Ratio Value = a / b
3. Calculate: 3 / 4 = 0.75
4. Result: The ratio value of 3:4 is 0.75

2. Reduce a Ratio

Example: Reduce the ratio 12:18

1. Identify the terms: a = 12, b = 18
2. Find the GCD of 12 and 18 (GCD = 6)
3. Divide both terms by the GCD: 12/6 : 18/6
4. Result: The reduced ratio is 2:3

3. Compare Ratios

Example: Compare the ratios 2:3 and 4:6

1. Calculate the value of the first ratio: 2/3 ≈ 0.667
2. Calculate the value of the second ratio: 4/6 ≈ 0.667
3. Compare the values
4. Result: The ratios are equal

4. Scale a Ratio

Example: Scale the ratio 3:4 by a factor of 2

1. Identify the terms: a = 3, b = 4
2. Multiply both terms by the scale factor: (3 × 2) : (4 × 2)
3. Calculate: 6:8
4. Result: The scaled ratio is 6:8

Visual Representation

Visual aids can help in understanding ratios. Here's a simple diagram showing the ratio 3:4:

This diagram illustrates how the ratio 3:4 relates to a whole. The blue portion represents 3 parts out of the total 7 parts (3 + 4).