What's the difference between a ratio and a fraction?

A ratio compares two quantities to show their relationship, while a fraction represents a part of a whole. However, a ratio can be written as a fraction. The ratio 3 : 4 means 'for every 3 of the first quantity, there are 4 of the second,' which is the same as the fraction \frac{3}{4}.

Do I always need to simplify a ratio?

Yes, ratios should always be simplified to lowest terms. This makes the relationship between the quantities clearer and easier to understand. For example, 6 : 8 and 3 : 4 represent the same ratio, but 3 : 4 is simpler.

Can a ratio be greater than 1?

Yes, a ratio can be greater than 1. For example, if player A scored 54 points and player B scored 36 points, the ratio of A's points to B's points is 3 : 2 (or \frac{3}{2} = 1.5). This means player A scored 1.5 times as many points as player B.

How do I find a missing value when I know a ratio?

Set up a proportion using the known ratio and solve for the unknown. For example, if boys : girls = 3 : 4 and there are 12 boys, you write \frac{3}{4} = \frac{12}{x} and cross-multiply to find x = 16 girls.

Ratio

A ratio compares two quantities to show their relationship, and can be written as a fraction or with a colon to help you scale or find missing values.

a : b = \frac{a}{b}

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What each symbol means

What Ratio takes

Symbol	Meaning
$a$	The first quantity in the ratio, representing the numerator when written as a fraction; if this is read as a total or sum instead, the comparison breaks down.
$b$	The second quantity in the ratio, representing the denominator when written as a fraction; if this is read as a total or sum instead, the comparison breaks down.

When to use it

You use a ratio when you need to compare how much of one quantity relates to another.

Level

Usually taught in: Pre-Algebra

Worked examples

1. Simplify a ratio to lowest terms

Problem

Simplify the ratio 6 : 8 and express it as a fraction.

$\frac{6}{8}$
Write the ratio 6 : 8 as a fraction.
$\frac{6 \div 2}{8 \div 2}$
The GCF of 6 and 8 is 2, so divide both the numerator and denominator by 2.
$\frac{3}{4}$
Calculate the simplified fraction.

Answer: $\frac{3}{4}$

Simplifying a ratio means writing it as an equivalent ratio in lowest terms. We divide both the numerator and denominator by their greatest common factor to find the simplest form.

2. Find a missing value using a ratio

Problem

If the ratio of boys to girls in a class is

3 : 4

, and there are 12 boys, how many girls are there?

$\frac{3}{4} = \frac{12}{x}$
Set up a proportion using the given ratio; if there are 12 boys and the ratio is $3 : 4$ , we can find the number of girls by solving for $x$ .
$3 \cdot x = 4 \cdot 12$
Cross-multiply to eliminate the fractions.
$3x = 48$
Multiply $4 \cdot 12$ to get 48.
$x = 16$
Divide both sides by 3 to solve for $x$ .

Answer: $x = 16 \text{ girls}$

When you know a ratio and one of the quantities, you can use a proportion to find the other quantity. This method scales the original ratio to match the new situation.

3. Express a real-world ratio in simplest form

Problem

During a basketball season, player A scored 54 points and player B scored 36 points. Express the ratio of player A's points to player B's points in simplest form.

$54 : 36$
Write the two quantities as a ratio in order: player A's points to player B's points.
$\frac{54}{36}$
Convert the ratio to fraction form.
$\frac{54 \div 18}{36 \div 18}$
The GCF of 54 and 36 is 18, so divide both numerator and denominator by 18.
$\frac{3}{2}$
Calculate the simplified fraction.

Answer: $\frac{3}{2} \text{ or } 3 : 2$

Ratios are useful for comparing real-world quantities. Simplifying the ratio shows the relationship in its most basic form: player A scored 3 points for every 2 points player B scored.

Common mistakes

Where Ratio usually goes wrong

The mistake	Why it is wrong	The fix
Writing the ratio $3 : 4$ as being the same as the ratio $4 : 3$	Order matters in a ratio; $3 : 4$ represents a different comparison than $4 : 3$ .	Always write the quantities in the same order they appear in the problem. If the problem says 'boys to girls', write boys first.
Writing a ratio as $10 : 15$ instead of simplifying it to $2 : 3$	Ratios should always be expressed in simplest form by dividing both numbers by their GCF so the relationship is clear.	Find the GCF of both numbers (in this case, 5) and divide each by it: $10 \div 5 = 2$ and $15 \div 5 = 3$ , giving you $2 : 3$ .
If a recipe has 2 cups flour and 3 cups water (5 cups total), writing the ratio of flour as $2 : 5$	A ratio compares the two specific quantities to each other, not one quantity to the total amount.	The ratio of flour to water is $2 : 3$ , not $2 : 5$ , because you compare flour directly to water.

Tips and when to use something else

Always simplify ratios to lowest terms using the greatest common factor.
Order matters—the ratio $2 : 3$ is different from $3 : 2$ .
Use Proportion when you know a ratio and one value and need to find a missing related value.
For scaling problems like enlarging a recipe, ratios help you multiply or divide all parts by the same number.

Related formulas

ProportionUse Proportion when two ratios are equal to find a missing value by cross-multiplying to solve equations with fractions.Greatest Common FactorThe Greatest Common Factor finds the largest whole number that divides evenly into two or more numbers, helping you simplify fractions.Equivalent FractionsMultiply or divide both parts of a fraction by the same non-zero number to create an equivalent fraction with the same value.Unit RateA unit rate is a ratio that compares a quantity to exactly one unit of measure, helping you compare values or find the cost per item.

Frequently asked questions

What's the difference between a ratio and a fraction?: A ratio compares two quantities to show their relationship, while a fraction represents a part of a whole. However, a ratio can be written as a fraction. The ratio $3 : 4$ means 'for every 3 of the first quantity, there are 4 of the second,' which is the same as the fraction $\frac{3}{4}$ .
Do I always need to simplify a ratio?: Yes, ratios should always be simplified to lowest terms. This makes the relationship between the quantities clearer and easier to understand. For example, $6 : 8$ and $3 : 4$ represent the same ratio, but $3 : 4$ is simpler.
Can a ratio be greater than 1?: Yes, a ratio can be greater than 1. For example, if player A scored 54 points and player B scored 36 points, the ratio of A's points to B's points is $3 : 2$ (or $\frac{3}{2} = 1.5$ ). This means player A scored 1.5 times as many points as player B.
How do I find a missing value when I know a ratio?: Set up a proportion using the known ratio and solve for the unknown. For example, if boys : girls = $3 : 4$ and there are 12 boys, you write $\frac{3}{4} = \frac{12}{x}$ and cross-multiply to find $x = 16$ girls.

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Reviewed 2026-09-18