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Arithmetic Expressions

Writing your own expression

You buy 2 samosas at ₹15 each. You buy 3 pens at ₹25 each. What is the bill?

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The order: 2 samosas, 3 pens.
Step 1 of 5
  1. The order: 2 samosas, 3 pens.
  2. Samosas: 2 × 15 = 30.
  3. Pens: 3 × 25 = 75.
  4. Add the terms: 30 + 75 = 105.
  5. Two friends order the same: 2 × 105 = 210.

The rule

The bill is ₹105.

Write one term for each item: how many × the price. Join the terms with +.

2 × 15 + 3 × 25

Here 2 × 15 is the samosas and 3 × 25 is the pens. Then 30 + 75 = 105.

Two friends order the same. Put the whole bill in brackets. Then the 2 multiplies both the samosas and the pens.

2 × (2 × 15 + 3 × 25)

Check the size with easy numbers. Two samosas near ₹15 each is near ₹30. Three pens near ₹25 each is near ₹75. So a bill near ₹100 is sensible.

Three orders at the stall
The orderThe lineComes to
2 samosas, 3 pens2 × 15 + 3 × 25105
4 cups of tea at ₹124 × 1248
A ₹40 notebook, ₹10 off40 − 1030

Watch out!

Two friends need brackets round the whole bill. 2 × 2 × 15 + 3 × 25 doubles only the samosas. It gives 135, not 210.

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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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