Multiplication as repeated addition

In the introduction you saw that 3 × 4 = 12. Now we'll look at where that 12 came from. No magic.

The same problem — two ways

You had three baskets with four apples each. You counted it two ways:

• Adding: 4 + 4 + 4 = 12
• Multiplying: 3 × 4 = 12

Both give the same answer. Multiplication is just a shorter way of adding the same number again and again.

How we read 3 × 4

We can read 3 × 4 as a recipe:

"Three groups of four" — take 3 groups with 4 in each.

So:

3 × 4 = 4 + 4 + 4 = 12

The first number (3) tells you how many groups. The second (4) tells you how many in each group.

Try it — without a calculator

4 × 2 = 2 + 2 + 2 + 2 = 8 5 × 3 = 3 + 3 + 3 + 3 + 3 = 15 2 × 6 = 6 + 6 = 12

See? If you don't remember the answer, you can always fall back on adding. That's your safety net.

Tip — fewer groups is sometimes easier

Look at 3 × 4 and 4 × 3:

• 3 × 4 = 4 + 4 + 4 = 12 (only 3 additions)
• 4 × 3 = 3 + 3 + 3 + 3 = 12 (4 additions)

The answer is the same, but one path is shorter. The one with fewer groups is shorter (smaller first factor). More on this in the next article.

Summary

• Multiplication is repeated addition of the same number.
• 3 × 4 means "3 groups of 4" = 4 + 4 + 4.
• If you don't remember the answer, fall back on adding.