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Arithmetic Expressions

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A shop chit — a small bill — says 3 × 25 + 40. What is it worth?

What this track covers

Arithmetic Expressions — lines of numbers and signs. You will learn to read each one. First, what is the chit worth?

  • Expression and value — a sum, and the number it equals.
  • Order — one line can give two answers if nobody agrees.
  • Terms — pieces that get added. Work out each piece, then add.
  • Brackets — finish the inside of a bracket first.
  • Tied signs — same level? Work from the left.
  • Turning round — + and × can swap. − and ÷ usually change the value.
  • One tray, two counts — split a tray, and the counts still match.
  • Writing your own — turn a real bill into one line.
  • Swap and regroup — terms can swap and regroup. The total stays.
  • Brackets away — a minus before a bracket flips the signs inside.
  • Compare by moves — see how each term moved. No adding needed.
  • Near 100 — split a number near 100 for a quick product.

Quick catch-up

Four earlier ideas help here. You do not need them first.

  • × and ÷ (Track Zero) — × counts equal groups fast. ÷ splits a total into groups.
  • Tiling a rectangle (Perimeter and Area) — rows times columns.
  • A good estimate (Number Play) — round the numbers first.
  • Moving past zero (Negatives) — 3 − 8 gives −5.

Jump to lesson

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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