Arithmetic Expressions
Tinkering with the terms
See what happens to an expression when you make one of its terms bigger or smaller.
What happens to an expression's value if you make one of its terms a little bigger or smaller? Know this, and lots of calculations become easy.
Start with 53 − 16 + 37 = 74. Change one term at a time:
| Change | Is the new term more or less? | New value |
|---|---|---|
| 53 → 54 | 1 more | 75 |
| 53 → 52 | 1 less | 73 |
| −16 → −15 | 1 more (closer to zero) | 75 |
| −16 → −17 | 1 less | 73 |
Think of a balance scale: both sides must stay equal. If you add something to one side, you must make up for it.
- 423 + ___ = 419 + ___: the left starts 4 ahead, so the right blank must be 4 more than the left blank.
- 207 − 68 = 210 − ___: the right starts 3 ahead, so it must take away 3 more: the blank is 71.
Jasoda's shortcut: to subtract 9, she subtracts 10 and adds 1: 36 − 9 = 26 + 1 = 27. Always right? Yes: she took away 1 too many, then put it back.
More tricks like it: subtract 99 by taking away 100 and adding 1; add 98 by adding 100 and taking away 2.
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