22 Part 1: The World of Numbers
You can use the add-back method of subtraction whenever it seems convenient, even if you’re not
making change. To subtract 5,250 – 3,825, you can start with 3,875 and think:
Adding 5 will make 3,830
Adding 20 will make 3,850
Adding 400 will make 4,250
Adding 1,000 will make 5,250
So 5,250 – 3,825 = 1,425.CHECK POINT
Complete each subtraction problem.- 596 – 312
- 874 – 598
- 1,058 – 897
14. 5,403 – 3,781
15. 14,672 – 5,839
Thinking of subtraction as adding back instead of taking away can be helpful for mental math.
If you buy something that costs $5.98 and give the cashier a $10 bill, how much change should
you get? Instead of doing all the borrowing and regrouping that’s necessary to subtract 10.00 –
5.98, start with $5.98 and think about what you’d need to add to get to $10. You’d need 2 pennies,
or $0.02, to make $6, and then another $4 to make $10. So your change should be $4.02.In our example of 418 – 293, you’ll look to the hundreds place of 418, where there are 4 hundreds,
and you’ll borrow 1 hundred. You’ll cross out the 4 and make it a 3, so you don’t forget that you
borrowed 1 hundred, and you’ll take that 1 hundred and change it back into 10 tens. You’ll add
those 10 tens to the 1 ten that was already in the tens place, and you’ll have 3 hundreds, 11 tens,
and 8 ones. Then you can take away 293, or 2 hundreds, 9 tens, and 3 ones. So 8 ones – 3 ones =
5 ones, 11 tens – 9 tens = 2 tens and 3 hundreds – 2 hundreds = 1 hundred. Here’s how it
would look:Borrowing isn’t always necessary, as you saw in the earlier example. When it is, you’ll find it’s
wise to mark the ungrouping you’ve done and not try to juggle it all in your head.418
293
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