Fractions and Ratios

Fractions and ratios are two ways of describing parts, proportions, and relationships between quantities. They show how one amount compares to another, whether you’re splitting something into pieces or comparing two values directly.

What fractions represent

A fraction shows part of a whole. It has a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.

Fraction = numerator / denominator

What ratios represent

A ratio compares two quantities directly. Instead of describing part of a whole, it shows how one amount relates to another. Ratios can be written with a colon, as a fraction, or in words.

Ratio = a : b

A simple example

If you have 2 slices of pizza out of 8, the fraction is 2/8. The ratio of slices you have to slices total is 2:8. Both describe the same relationship, just in different formats.

Simplifying fractions and ratios

Fractions and ratios can often be simplified by dividing both numbers by a common factor. In the example above, 2/8 simplifies to 1/4, and the ratio 2:8 simplifies to 1:4. The relationship stays the same — only the expression changes.

Common misconceptions

• “Fractions and ratios are unrelated.” They describe similar relationships in different formats.
• “A bigger denominator means a bigger fraction.” A larger denominator means smaller pieces, not a larger value.
• “Ratios must use whole numbers.” Ratios can compare any quantities, including decimals.

Fractions and ratios are powerful tools for describing parts and proportions. Once you understand how they work, comparing quantities becomes much more intuitive.