3rd grade · 12 facts · division

Dividing by 1

Dividing by 1 leaves a number as it is: 8 ÷ 1 = 8 and 12 ÷ 1 = 12. Share 8 cookies with one person and that person gets all 8. It is the division side of the 1 times table, and children usually find it easy once they hear it as a sharing story.

What deserves time on this page is the difference between dividing by 1 and dividing a number by itself. 6 ÷ 1 = 6, but 6 ÷ 6 = 1. The two look alike, and mixing them up is one of the first slips children make with division.

All 12 divide-by-1 facts

  • 1 ÷ 1 = 1
  • 2 ÷ 1 = 2
  • 3 ÷ 1 = 3
  • 4 ÷ 1 = 4
  • 5 ÷ 1 = 5
  • 6 ÷ 1 = 6
  • 7 ÷ 1 = 7
  • 8 ÷ 1 = 8
  • 9 ÷ 1 = 9
  • 10 ÷ 1 = 10
  • 11 ÷ 1 = 11
  • 12 ÷ 1 = 12

Every fact here divides evenly. Division with remainders comes in 4th grade.

Printable practice sheet (PDF) — 24 problems: the 12 facts in order, then the same facts mixed up. The answer key is on page 2. Free to print, no sign-up.

Timed drill: dividing by 1

12 facts in a random order. A right answer within 3 seconds counts as by heart. Free, no sign-up, and nothing is saved: it all happens on this screen.

Type with the keypad or your keyboard, then press Check or Enter.

What to notice

Every fact on the list below ends with the number it started with: 1 ÷ 1 = 1, 2 ÷ 1 = 2, all the way to 12 ÷ 1 = 12. Each one is the 1 times table read backwards: because 1 × 9 = 9, you know 9 ÷ 1 = 9.

Division can be asked two ways, and both work here. “Share 7 among 1” asks how many each gets: 7. “How many groups of 1 are in 7?” asks how many groups: also 7. Later tables give the same answer both ways too, but the two questions feel different to a child, so it helps to meet them first where the answer is easy.

Zero has its own rules. 0 ÷ 1 = 0: sharing nothing gives nothing. But 1 ÷ 0 has no answer at all, because no number of empty groups ever adds up to 1. Your child does not need the full reason yet; it is enough to know that dividing by zero is not allowed.

How to practise at home

  • Act it out with one cup. Put 5 buttons in it and ask how many are in the cup. Then use two cups and share the 5 again, to feel the difference dividing by 2 makes.
  • Ask the pair together: 9 ÷ 1 and then 9 ÷ 9. Hearing them back to back is a good way to stop the mix-up before it starts.
  • Write one fact family out in full: 1 × 4 = 4, 4 × 1 = 4, 4 ÷ 1 = 4 and 4 ÷ 4 = 1. It shows how the four facts belong together, and it is the same shape every later family will take.
  • Use the drill on this page as a short warm-up. It should feel easy; if it does not, go back to the sharing story.

Slips to watch for

  • Answering 1 for 7 ÷ 1, which mixes it up with 7 ÷ 7. Ask “share 7 with how many people?”
  • Reading 1 ÷ 5 as if it were 5 ÷ 1. In division the order matters, unlike multiplication: 5 ÷ 1 is 5, but 1 ÷ 5 is one fifth, a fraction your child will meet later in 3rd grade.
  • Believing division always makes a number smaller. Dividing by 1 is the first exception, and a good moment to say that rules like “division shrinks things” have limits.

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