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Simplified Ratio
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Enter values to calculate
Decimal
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A % of Total
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B % of Total
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GCD
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Simplify a ratio to its lowest terms, solve for a missing value in a proportion (A:B = C:?), or split a total quantity into parts according to a given ratio.

How It Works

How Ratio Calculator Works

Simplifying a ratio works by finding the greatest common divisor (GCD) of its terms and dividing every term by it — exactly the same principle as reducing a fraction to lowest terms, since a ratio a:b is mathematically equivalent to the fraction a/b.

Solving a proportion A:B = C:D relies on cross-multiplication: since A/B equals C/D, the missing value D can be found directly as D = B×C/A.

Dividing a quantity according to a ratio first adds up all the ratio's terms to get a total number of equal "shares," then allocates the full quantity proportionally — each part's share equals the total quantity multiplied by (that part's ratio value ÷ the sum of all ratio values).

Worked Example

See It In Action

Simplifying the ratio 6:4 — the GCD of 6 and 4 is 2 — gives 3:2, equivalent to a decimal of 1.5 (6÷4). As percentages of the whole, that split is 60% and 40% respectively.
Real-World Use Cases

Who Uses Ratio Calculator and Why

  • Simplifying a recipe or paint-mixing ratio down to its lowest terms.
  • Solving for a missing value in a scale-model or map proportion, like A:B = C:?
  • Splitting a shared expense or profit among partners according to an agreed ratio.
  • Converting a two-part ratio into percentages of the whole for a presentation or report.
Common Mistakes

Mistakes to Avoid

  • Treating a multi-term ratio (like 2:3:5) the same as a simple two-term fraction, when the underlying share-based math needs every term accounted for.
  • Forgetting that splitting a quantity by ratio treats the ratio's terms as a number of equal shares that sum together first, not as direct percentages of the final quantity.
  • Cross-multiplying the wrong pair of terms when solving a proportion, which produces an incorrect missing value.
Pro Tips

Tips for Best Results

  • After simplifying a ratio, check that dividing both original terms by the same GCD reproduces your simplified result — a quick way to catch entry mistakes.
  • When splitting a total by a ratio, remember each 'share' is worth the total quantity divided by the sum of all the ratio's terms.
Troubleshooting

Fixing Common Problems

My split amounts don't add back up to the original total. — Double-check the ratio terms were entered in the correct order matching each part — a mismatched order produces amounts that don't correspond to the intended split.

Glossary

Terms Explained

Greatest common divisor (GCD): The largest number that divides every term of a ratio evenly, used to reduce it to lowest terms.

Proportion: A statement that two ratios are equal, such as A:B = C:D, solvable for a missing term via cross-multiplication.

FAQ

Frequently Asked Questions

How is a ratio simplified to lowest terms?
Both sides of the ratio are divided by their greatest common divisor (GCD) — for 6:4, the GCD is 2, so dividing both terms by 2 gives the simplified ratio 3:2.
How do I solve a proportion like 3:4 = 6:?
Cross-multiply: the missing value equals (4 × 6) ÷ 3 = 8, so the completed proportion is 3:4 = 6:8 — both sides reduce to the same 0.75 decimal ratio.
How does splitting a quantity by ratio work?
Splitting $100 in a 2:3 ratio treats the ratio as 5 equal shares total (2+3); each "share" is worth $100÷5=$20, so the split is $40 (2 shares) and $60 (3 shares).
Is a ratio the same thing as a fraction?
They're closely related — a two-term ratio a:b behaves mathematically like the fraction a/b — but a ratio compares two or more separate quantities to each other, while a fraction represents a part relative to a whole.