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# Mental subtraction strategies 2: place value; difference; use an easier problem

### See also

In the video below, I show two simple examples of subtracting 3-digit numbers mentally. We can use our knowledge of place value to do these subtractions. For example, to subtract 652 − 30, notice that we're subtracting three tens. So, we look at the TENS digit in 652 and subtract 5 − 3 (in the tens). If a child understands place value, subtractions such as 478 − 20 or 783 − 200 are easy. If a child has difficulty with them, it typically indicates the child has not understood the concept of place value (hundreds, tens, ones).

In the video below, we look at several subtraction problems (2-digit and 3-digit) where the most effective strategy is to think of the difference between the numbers. This strategy works best when the numbers to be subtracted are close to each other.

The last example we look at is the two-digit subtraction 72 − 37. I solve it by finding the difference between 37 and 72 — essentially "adding up" from 37 to 72, in three different parts. I show arrows with jumps — like using a number line without tick marks.

Here, instead of subtracting 29 from 66, we can subtract 30. It makes for a much easier problem to solve! Lastly, we adjust the answer, because in subtracting 30 instead of 29, we subtracted one too much. This is a really neat strategy and works for many kinds of problems, such as 99 + 87 or 4031 − 999.

More mental addition and subtraction — with 3-digit numbers

Math Mammoth Grade 3 curriculum