---
title: "How to Calculate Ratios and Proportions — Simplify, Solve, Scale"
description: "Learn to simplify ratios, solve proportions with cross-multiplication, scale recipes, read map scales, and understand exchange rates. Step-by-step with real examples."
url: "https://worldcalculators.org/learning/how-to/ratios-proportions/"
canonical: "https://worldcalculators.org/learning/how-to/ratios-proportions/"
---

# How to Calculate Ratios & Proportions

Learn to simplify ratios, solve proportions with cross-multiplication, scale recipes, read map scales, and understand exchange rates. Step-by-step with real examples.

## Quick answer

Simplify a ratio: divide both numbers by their GCD. 24:36 → GCD=12 → 2:3 . Solve a proportion: cross-multiply. If 3/4 = x/20 → x = (3×20)/4 = 15 . Scale a recipe: multiply every ingredient by (new servings ÷ old servings). Recipe for 4 → serving 10: multiply by 2.5.

## Part 1: Simplifying Ratios

A ratio compares two (or more) quantities. 12:8 means "12 for every 8" — but 3:2 says the same thing more simply.
The largest number that divides evenly into both. For 12 and 8: factors of 12 = 1,2,3,4,6,12. Factors of 8 = 1,2,4,8. GCD = 4.

## Part 2: Solving Proportions (Cross-Multiplication)

A proportion is two equal ratios: a/b = c/d. Cross-multiply: a × d = b × c, then solve for the unknown.
Example: If 5 apples cost $3, how much do 8 apples cost?

## Real-World Applications

Multiply all ingredients by (new servings ÷ original servings). Recipe for 4, need 6: factor = 1.5. Every ingredient × 1.5.
Scale 1:50,000 means 1 cm on map = 50,000 cm = 500 m in reality. 4 cm on map → 4 × 500 = 2,000 m = 2 km real distance.

Source: https://worldcalculators.org/learning/how-to/ratios-proportions/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.