Division as sharing

In the introduction we saw that 12 ÷ 3 = 4. Now let's see how it actually works when you do it with your hands.

One into each pile

Picture 12 sweets and 3 bowls. How do you share them fairly?

The easiest way: deal them one at a time into each bowl, going round and round.

• 1st sweet → bowl A
• 2nd sweet → bowl B
• 3rd sweet → bowl C
• 4th sweet → bowl A (and start over)
• ...until you've run out of sweets.

When you're done, every bowl has the same count — 4. That's the answer: 12 ÷ 3 = 4.

What we're doing mathematically

Division is repeated subtraction of the same number. In 12 ÷ 3:

12 − 3 = 9 (we took 3 sweets, one for each bowl)

9 − 3 = 6 (second round)

6 − 3 = 3 (third round)

3 − 3 = 0 (fourth round)

We subtracted 3 four times → every bowl has 4 sweets.

But in practice you don't count this way. Knowing your times tables is enough — more in the next articles.

Try it yourself

8 ÷ 2 = ? Picture 8 building blocks and 2 children. You deal one at a time.

• A, B, A, B, A, B, A, B → each has 4.
• 8 ÷ 2 = 4.

15 ÷ 5 = ? 15 cookies for 5 children.

• A, B, C, D, E (×3) → each has 3 cookies.
• 15 ÷ 5 = 3.

When it doesn't share evenly

If you have 13 sweets and 3 bowls, you manage to share 12 of them (4 in each bowl), but 1 sweet is left over. We call this division with a remainder.

In 2nd grade we'll only give you problems that come out exactly — no remainder. Remainders come later.

Summary

• Division is splitting into equal piles.
• If you deal one item at a time into each pile, going round and round, every pile ends up the same — or nearly the same (with a remainder).
• In 2nd grade we only do division without remainders for now.
• Division can also be seen as repeated subtraction.