Working with Ratios

Ratios express the quantitative relationship between two values and are fundamental in countless real-world applications from scaling recipes in cooking to maintaining proportions in architectural designs.

How to Simplify Ratios

Divide both numbers by their greatest common divisor (GCD)
Maintain the same proportion between numerator and denominator
Express the result as whole numbers when possible

Practical Examples

Recipe Scaling Example:

A cookie recipe uses 2 cups of flour to 1 cup of sugar (2:1 ratio). To double the recipe, simply multiply both values by 2 → 4 cups flour : 2 cups sugar.

Common Ratio Reference

Original Ratio	Simplified	Common Use
16:20	4:5	Screen resolutions
9:15	3:5	Photo printing

Important Tip:

Always maintain consistent units when working with ratios. Comparing 300 grams to 1 kilogram requires converting to same units first (300g:1000g → 3:10).

Frequently Asked Questions

What is a ratio in simplest form?

A ratio in simplest form has both terms reduced to the smallest whole numbers possible while maintaining the same proportion. For example, 8:12 simplifies to 2:3.

How do I scale a ratio?

Multiply both values by the same scaling factor. For example, to scale 2:3 by factor 5, multiply both terms (2×5:3×5) to get 10:15.

Can ratios have decimals?

While ratios are typically expressed as whole numbers, decimal values are mathematically valid. However, for practical applications, it's usually better to convert to whole numbers by multiplying by an appropriate factor.

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Ratio Calculator - Simplify Ratios and Scale Values

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