Foundational math vocabulary
Multiplication
Pronunciation: mul-tuh-pluh-KAY-shun
Multiplication combines equal groups or scales one quantity by another.
×·Foundational
Plain language
What it means
Multiplication combines equal groups or scales one quantity by another.
Formal meaning
Mathematical definition
For numbers a and b, the product ab represents repeated addition for whole numbers and extends to scaling for other number systems.
Where it fits
Its place in mathematics
Multiplication supports area, rates, proportions, algebra, exponents, probability, and unit conversion.
Why it matters
The practical reason to learn it
It makes repeated addition efficient and describes how quantities grow or shrink by factors.
Worked example
Multiply using decomposition
Use decomposition to find the product 23 × 14.
- Decompose 14 as 10 + 4.
- Compute 23 × 10 = 230 and 23 × 4 = 92.
- Add the partial products.
23 × 14 = 322.
Real-life example
Where this appears
A cook scales every ingredient when doubling or halving a recipe.
Common mistake
What to watch for
Treating multiplication only as repeated addition, which becomes awkward for fractions, decimals, negative numbers, and scaling.
Memory tip
Keep this in mind
Read a × b as a groups of b, then also picture it as a scale factor.
Little-known fact
Keep curiosity alive
Multiplication is commutative for ordinary numbers but matrix multiplication generally is not.
A profession that uses this idea
Scaling keeps quantities consistent
Cooks and business owners multiply unit amounts by the number of servings or items needed.
Explore Merchants & Business OwnersFollow the learning trail
Prerequisites, related ideas and next concepts
People behind the ideas
Related Math Heroes
Fibonacci
A Pisan mathematician whose Liber Abaci promoted efficient calculation with Hindu-Arabic numerals for trade, conversion, interest, and mathematical problems.
Yang Hui
Yang Hui was mathematician and teacher. His books preserved algorithms, magic squares, root extraction, and the triangular arrangement of binomial coefficients.
Put the idea to work