Foundational math vocabulary

Fraction

Pronunciation: FRAK-shun

A fraction represents equal parts of a whole, a ratio, or one number divided by another.

Symbols and notationa/b
Subject
Grade bands
Difficulty

Foundational

Profession trailCarpenters & Builders

Plain language

What it means

A fraction represents equal parts of a whole, a ratio, or one number divided by another.

Formal meaning

Mathematical definition

A fraction a/b is a rational number when a and b are integers and b is not zero.

Where it fits

Its place in mathematics

Fractions connect whole-number arithmetic to decimals, percentages, rates, proportions, algebra, and probability.

Why it matters

The practical reason to learn it

They describe exact parts and relationships that whole numbers alone cannot express.

5 shaded parts out of 8
Equal parts of one wholeThe denominator names the number of equal parts; the numerator counts the parts being considered.

Worked example

Add related fractions

Find 3/8 + 2/8.

  1. The denominators match, so add the numerators.
  2. Keep the common denominator.
Answer

3/8 + 2/8 = 5/8.

Real-life example

Where this appears

A carpenter measures board lengths in halves, quarters, eighths, and sixteenths of an inch.

Common mistake

What to watch for

Adding denominators when adding fractions with a common denominator. The size of the parts does not change.

Memory tip

Keep this in mind

Say the denominator as the part size and the numerator as the count.

Little-known fact

Keep curiosity alive

Every terminating decimal and repeating decimal represents a fraction.

A profession that uses this idea

Precise cuts use fractional measurement

Carpenters read and combine fractional lengths when laying out and cutting materials.

Explore Carpenters & Builders

Follow the learning trail

Prerequisites, related ideas and next concepts

Learn first

Related terms

Learn next

People behind the ideas

Related Math Heroes

Ahmes

An Egyptian scribe whose surviving copy of an older mathematics text preserves arithmetic, fractions, measurement, and practical problem solving from the ancient world.

Fibonacci

A Pisan mathematician whose Liber Abaci promoted efficient calculation with Hindu-Arabic numerals for trade, conversion, interest, and mathematical problems.

Put the idea to work

Related practice