Compare without working it out
Two bills: 512 + 347 and 514 + 342. Which is bigger? You need not add.
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Step 1 of 5
- The two sums: 512 + 347 and 514 + 342.
- The first term went from 512 to 514. It rose by 2.
- The second term went from 347 to 342. It fell by 5.
- The moves push the value +2 and −5. That is −3.
- So 514 + 342 is 3 less than 512 + 347.
The rule
The first bill is bigger, by 3.
Find how far each term moved. Each move pushes the value. A push is how much the value rises or falls.
A term you add pushes the value the way it moved. A term you take away pushes the value the other way.
Add the pushes. If the total push is 0, the two lines are equal.
A sum stays equal when one term gains what the other loses.
A difference stays equal when both terms move by the same amount.
For a difference, up 2 and up 2 keep it equal. Up 2 and down 2 do not.
| The two lines | First term | Second term | The second line is |
|---|---|---|---|
| 640 + 250 and 643 + 247 | up 3 | down 3 | equal |
| 640 + 250 and 645 + 250 | up 5 | no move | bigger |
| 540 − 120 and 542 − 122 | up 2 | up 2 | equal |
| 540 − 120 and 542 − 118 | up 2 | down 2 | bigger |
| 540 − 120 and 541 − 125 | up 1 | up 5 | smaller |