Foundational math vocabulary

Multiplication

Pronunciation: mul-tuh-pluh-KAY-shun

Multiplication combines equal groups or scales one quantity by another.

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Subject
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Difficulty

Foundational

Profession trailMerchants & Business Owners

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.

Rows, columns, and areaA rectangular array shows multiplication as equal rows and equal columns.

Worked example

Multiply using decomposition

Use decomposition to find the product 23 × 14.

  1. Decompose 14 as 10 + 4.
  2. Compute 23 × 10 = 230 and 23 × 4 = 92.
  3. Add the partial products.
Answer

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.

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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.

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