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Arithmetic Expressions

When two signs tie, take the left one

A chit — a small bill — says 24 ÷ 4 × 2. One order gives 12. The other gives 3.

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The line: 24 ÷ 4 × 2.
Step 1 of 6
  1. The line: 24 ÷ 4 × 2.
  2. Left first: 24 ÷ 4 = 6.
  3. Then 6 × 2 = 12.
  4. Right first: 4 × 2 = 8.
  5. Then 24 ÷ 8 = 3.
  6. Agreed answer: 12.

The rule

× and ÷ are on the same level. So are + and −. Signs on one level have the same rank.

With two signs on one level, the signs cannot decide. Do the left one first. That is the agreed rule.

For 24 ÷ 4 × 2, first 24 ÷ 4 = 6. Then 6 × 2 = 12.

The same is true for + and −. In 50 − 20 + 5, first 50 − 20 = 30. Then 30 + 5 = 35.

Four lines with a tie, and both orders
The lineLeft firstRight firstAgreed
24 ÷ 4 × 212312
100 − 30 − 20509050
36 ÷ 6 ÷ 32182
2 × 6 ÷ 3444

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This track

  1. 0 Start here
  2. 1 An expression and its value
  3. 2 The order changes the answer
  4. 3 Work out each term first
  5. 4 Brackets go first
  6. 5 When two signs tie, take the left one
  7. 6 What you may turn round
  8. 7 One tray, counted two ways
  9. 8 Writing your own expression
  10. 9 Swap and regroup the terms
  11. 10 Taking the brackets away
  12. 11 Compare without working it out
  13. 12 Split a number near 100
  14. 13 Checkpoint
  15. 14 The big picture
  16. 15 Track quiz

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