Foundational math vocabulary
Fraction
Pronunciation: FRAK-shun
A fraction represents equal parts of a whole, a ratio, or one number divided by another.
a/bFoundational
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.
Worked example
Add related fractions
Find 3/8 + 2/8.
- The denominators match, so add the numerators.
- Keep the common denominator.
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 & BuildersFollow the learning trail
Prerequisites, related ideas and next concepts
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