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MentalMathsWorkbook - Subtracting two digit numbers.

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As we did with the two digit additions, our goal should be to simplify the subtraction to two or more single digit additions or subtractions.

When we subtract a number from another, the subtraction might involve a borrow. When this happens, we need to remember the borrow. For example, consider the following subtraction:

x

Note that in the above example, 18 is the subtrahend and 43 is the minuend.

The problem is a bit complex to do in the head because we have to borrow from the tens place (4) when we go to subtract the units place digits (i.e. subtracting 8 from 3). However, we can simplify the problem to:

x

Which breaks down into the following two steps:

Step 1. Subtract 20 from 43

x

Step 2. Since we have subtracted 2 more than we were supposed to (we subtracted 20 instead of 18), we now add 2 to the result from step 1.

x

The above technique can be applied when there is a borrow involved.

When there is no borrow involved, we can conceptually think of subtractions as two-step process. For example:

x

Which breaks down into the following two steps:

Step 1. Subtract 20 from 67

x

Step 2. Subtract 6 from the result from step 1.

x

Which is just like the normal subtraction process, except that it is done left to right. This makes it easier to do in the head.

The above two techniques can be applied to three digit subtractions also. For example:

x

That is, in the first step we subtract 400 from 622 to arrive at 222. To that, we need to add 7 to arrive at the final answer 229.

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