Ratio Calculator — Simplify Ratios & Solve Proportions
Simplify ratios (a:b) and solve proportions (a:b = c:?). Shows simplified ratio, equivalent ratios, and step-by-step solution.
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Simplified Ratio
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As Fraction
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As Decimal
Steps & Equivalent Ratios
Frequently Asked Questions
What is a ratio?
A ratio compares two quantities by division. The ratio a:b means "a for every b". For example, a ratio of 3:4 means for every 3 of something, there are 4 of something else. Ratios can be expressed as fractions, decimals, or with a colon.
How do you simplify a ratio?
Divide both parts by their HCF (Highest Common Factor). For example, 12:18 — HCF(12,18) = 6 — simplified to 2:3. A simplified ratio has no common factors other than 1.
What is a proportion?
A proportion states that two ratios are equal: a/b = c/d. This is read "a is to b as c is to d." You can solve for any unknown using cross multiplication: if a/b = c/d, then ad = bc.
How do equivalent ratios work?
Equivalent ratios represent the same comparison. For example, 1:2, 2:4, 3:6, and 4:8 are all equivalent. Multiply or divide both parts of a ratio by the same non-zero number to create equivalent ratios.
What is the difference between ratio and fraction?
A fraction a/b represents a part of a whole (where b is the total), while a ratio a:b compares two separate quantities. However, ratios can be converted to fractions: a:b = a/(a+b) : b/(a+b).