Multiplication as Repeated Addition

About this topic

Multiplication is a fast way of adding the same number many times: 3 × 4 means three added four times, or four groups of three. Seeing it as an array of rows and columns also shows why the area of a rectangle is length times width.

Multiplication is commutative, so 3 × 4 = 4 × 3, and associative, and any number times one stays unchanged while any number times zero is zero. It also distributes over addition, so 6 × 14 can be done as 6 × 10 + 6 × 4 = 60 + 24 = 84. Memorising the times tables frees your attention for harder problems later, such as fractions, algebra and factoring.

Picture a classroom with 7 rows of 8 desks. Counting every desk would be slow, but 7 × 8 = 56 gives the total at once. A grid of dots makes the same point visually and shows that rotating the grid does not change the count. The same idea works for pricing: 12 items at 5 dollars each cost 60 dollars.

Multiplication powers area, scaling recipes, unit conversions, interest and probability. A common misconception is that multiplication always makes numbers bigger. That is true for whole numbers above one, but multiplying by a fraction less than one makes a number smaller, and multiplying by a negative flips its sign. Learning patterns, like the nines facts whose digits sum to nine, helps memory.