Many equal groups
What Does Multiplying Do?
Multiplication is adding the same number over and over, done in one move.
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Step 1 of 5
It only works when the groups are equal.
Multiplication is the shortcut you earn by making the groups match. Four bags with three apples each is 4 × 3. If the bags held different amounts, multiplication would not apply — you would have to add.
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Step 2 of 5
It is repeated addition, compressed.
3 + 3 + 3 + 3 = 12, and so does 4 × 3. For four groups the saving is small. For four hundred groups it is enormous.
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Step 3 of 5
Order does not matter.
The counters never moved. Only the way you described them did. 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.
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Step 4 of 5
Multiplying by 1 and 0 are special.
One group of seven is seven. Zero groups of seven is nothing at all. These two rules catch people out constantly.
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Step 5 of 5
Splitting numbers up makes it easy.
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.