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Ratio Calculator

Simplified Ratio

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Includes your inputs and results for this calculation, plus any additional calculations you've compared.

How This Calculator Works

A ratio compares two quantities, and simplifying it means writing it with the smallest whole numbers that keep the same relationship. Enter two numbers to simplify their ratio to lowest terms, or enter three numbers of a proportion (A is to B as C is to what?) to solve for the missing fourth term.

The Formula

Simplifying a ratio: divide both numbers by their greatest common factor (GCF) — the largest whole number that divides evenly into both.

Solving a proportion (A:B=C:D\vA{A}:\vB{B} = \vC{C}:D): cross-multiplication gives A×D=B×C\vA{A} \times D = \vB{B} \times \vC{C}, so the missing term is:

D=B×CAD = \frac{\vB{B} \times \vC{C}}{\vA{A}}

Worked Example

Simplifying 8:12:

  1. Greatest common factor of 8 and 12: 4.
  2. Divide both parts by 4: 8÷4:12÷4=2:38 \div 4 : 12 \div 4 = 2 : 3.

Solving 4:6 = 10:?

  1. Cross-multiply: ?=6×104? = \frac{6 \times 10}{4}.
  2. ?=604=15? = \frac{60}{4} = 15, so 4:6 = 10:15.

Source: Standard ratio simplification and cross-multiplication proportion methods.

Frequently Asked Questions

How do you simplify a ratio?

Divide both numbers by their greatest common factor (GCF) — the largest whole number that divides evenly into both. For example, 8:12 simplifies to 2:3 by dividing both by their GCF of 4.

What does "solve a proportion" mean?

A proportion states that two ratios are equal (A:B = C:D). If you know three of the four numbers, cross-multiplication (A x D = B x C) lets you solve for whichever one is missing.

Does a ratio have to use whole numbers?

Simplifying a ratio to lowest terms specifically assumes whole numbers, the same way simplifying a fraction does. Solving a proportion, on the other hand, works with any real numbers, including decimals.