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Operations with Integers

What zero does

Take 7 + 0, 7 × 0, 0 ÷ 7 and 7 ÷ 0. One has no answer. Which?

7 + 0 = 7. No steps taken.
Step 1 of 4
  1. 7 + 0 = 7. No steps taken.
  2. 7 × 0 = 0. Nothing, seven times.
  3. 0 ÷ 7 = 0. Nothing shared seven ways.
  4. 7 ÷ 0 has no answer.

Only 7 ÷ 0 has no answer.

Rule: adding or taking away zero changes nothing. Times zero is zero. Zero shared into some groups is zero. Sharing into zero groups has no answer.

0 − 7 is not the same as 7 − 0. Taking away 0 changes nothing, so 7 − 0 = 7. Start at zero and walk 7 left: 0 − 7 = −7.

7 ÷ 0 asks: how many empty groups make a pile of 7? An empty group holds nothing. So no count of empty groups makes a pile of 7. That is why 7 ÷ 0 has no answer.

Slide the groups down to 0 in the lab. See which count has no answer.

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This track

  1. 0 Start here
  2. 1 Two moves the same way
  3. 2 A move each way
  4. 3 Taking away, another way round
  5. 4 Two dashes on one line
  6. 5 Without the line
  7. 6 Checkpoint: adding and taking away
  8. 7 The same move, counted again
  9. 8 Past the end of the times table
  10. 9 Sharing it out
  11. 10 What zero does
  12. 11 Where we use them
  13. 12 Checkpoint: multiplying, sharing and zero
  14. 13 Zero pairs
  15. 14 The additive inverse
  16. 15 Many numbers, one sign
  17. 16 A number times a bracket
  18. 17 The big picture
  19. 18 Track quiz

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