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ELI5 Yahaaa

Many equal groups

What Does Multiplying Do?

Multiplication is adding the same number over and over, done in one move.

1 Groups of thesame size2×How manygroups?3 The total, inone move
Addition's shortcut for equal groups.

  1. Step 1 of 5

    It only works when the groups are equal.

    Unequal groups Must add themindividuallyEqual groups Multiply

    Four bags with three apples each is 4 × 3. If the bags held different amounts, multiplication would not apply — you would have to add.

  2. Step 2 of 5

    It is repeated addition, compressed.

    400 groups: adding400 steps400 groups: multiplying1 step4 groups: adding4 steps

    3 + 3 + 3 + 3 = 12, and so does 4 × 3. For four groups the saving is small. For four hundred groups it is enormous.

  3. Step 3 of 5

    Order does not matter.

    4 rows of 3 123 rows of 4 Still 12

    4 × 3 and 3 × 4 both give 12. Turn the grid on its side to see why — the counters do not change, only your description of them.

  4. Step 4 of 5

    Multiplying by 1 and 0 are special.

    × 11Nothing changes× 00Everything becomesnothing

    One group of seven is seven. Zero groups of seven is nothing at all. These two rules catch people out constantly.

  5. Step 5 of 5

    Splitting numbers up makes it easy.

    1 7 × 122 7 × 10 = 70, 7× 2 = 143=70 + 14 = 84

    For 7 × 12, do 7 × 10 = 70 and 7 × 2 = 14, then add: 84. Every mental multiplication trick is a version of this.

    The × symbol was introduced in 1631. Some mathematicians objected because it looked too much like the letter x.

The short version

Multiplication is repeated addition of equal groups, compressed into one step.

Try it yourself

Count the windows on a building by counting one row and one column, then multiplying. Far faster than counting them all.

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