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MentalMathsWorkbook - Subtractions with borow


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Suppose you wanted to eat candy. You know that your mother has 12 candies

Candy Candy Candy Candy Candy Candy Candy Candy Candy Candy Candy Candy
1 2 3 4 5 6 7 8 9 10 11 12

and she gave you 3.

Candy Candy Candy
1 2 3

This is represented in math like this:


So, essentially, we need to subtract 3 from the original box of candies 12. In the number 12, the 1 is in the tens place and the 2 is in the units. To subtract a number from another number, we write the numbers so that the units places of the two numbers are in a line and the tens digits are also in a line. In the figure above, we wrote the 3 below the 2 of 12 (that is, the units places are aligned).

However, we notice that we can not subtract 3 from 2 because 3 is larger than 2. How can you take 3 candies from your mother if she had only 2 candies? So, we need to borrow from the tens place.

In the above example, 12 is called the minuend and 3 is the subtrahend. The result is called the difference.

Now consider the following subtraction:


Once again, the units place of the 32 and the units place of 15 aligned below. We will subtract the units place of 15 from the the units place of 32. Once again, we can see that we can't subtract 5 from 2. So, we need to borrow 1 from 3. Now, the units place becomes 12 and we can easily subtract 5 from 12 to give 7. So, the units place of the result is a 7.

Next, we subtract the tens places. However, because we borrowed one from 3, we now are left with 2, and we need to subtrace 1 from 2, giving the final answer, 17.

To do the subtraction in your head without having to remember the to subtract the borrow, use this trick. Suppose you want to subtract 15 from 32. We can round up 15 to the next power of 10, i.e. 20 and do the subtraction in two steps.

  1. Round up the subtrahend to the next power of 10. In the current example, round 15 up to 20.
  2. Subtract the rounded number from the minuend. This is simple, giving 12.
  3. Add the number used to round up the subtrahend (i.e. 5 in this example) back to the result of the previous step, giving the correct answer.

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