All four operations, step by step

The last step in fact fluency is a page that gives no clue about which operation is coming next.

The question

30 ÷ 10

30÷10
10×?=30
10×3=30
30÷10=3
3×10=30
  1. 30 ÷ 10 means sharing 30 out equally between 10. Deal them round one at a time until they run out; the answer is how many end up in one share.
  2. Dealing out 30 one at a time works, and takes all day. The shortcut is the same fact read backwards: 10 shares of WHAT makes 30?
  3. 10 × 3 = 30. That is the one, so 30 ÷ 10 = 3.
  4. Worth checking, because it costs one multiplication: 3 × 10 = 30. It matches, so the answer holds.

How it works.

  1. 01

    30 ÷ 10 means sharing 30 out equally between 10. Deal them round one at a time until they run out; the answer is how many end up in one share.

  2. 02

    Dealing out 30 one at a time works, and takes all day. The shortcut is the same fact read backwards: 10 shares of WHAT makes 30?

  3. 03

    10 × 3 = 30. That is the one, so 30 ÷ 10 = 3.

  4. 04

    Worth checking, because it costs one multiplication: 3 × 10 = 30. It matches, so the answer holds.