Subtraction of Decimal Fractions

This topic will deal with subtraction of decimal fractions. As we did addition of decimal fractions in a similar way we will do subtraction of decimal fractions. First we need to change the set of fractions into like fractions and then write each of the decimal numbers in column. The decimal point should be in one vertical line. Then we need to subtract ignoring the decimal point. After subtraction is done we need to put the decimal point in proper place.

For example:

Subtract 75.02 from 87

First change the two decimal numbers into like fraction

75.02 and 87.00

                        6      9  10

                 8  7  .  0   0

              -   7  5  .  0   2

                  1  1  .  9   8

In the hundredths place we cannot subtract 2 from 0 and hence needs to borrow 1 from tenths place. But there is 0 in the tenths place and hence need to borrow 1 from units place to make the number in tenths place 10 and it will lend 1 from it to hundredths place and hence would become 9. Now in the hundredths place 2 can be subtracted from 10 after borrowing. In the hundredths place 0 can be subtracted from 9 to get 9.

The number in the units place is now 6 after lending. However 5 can be subtracted from 6 to get 1 and lastly in tens place 7 can be subtracted from 8 to get 1.

Here are few other examples on subtraction of decimals

1. Subtract 400.23 from 684. 9

Solution:

First change the two decimal numbers into like fraction

400.23 and 684.90

                                    8  10

                 6  8  4  .  9   0

             -    4  0  0  .  2   3

                  2  8  4  .  6   7

In this subtraction in hundredths place 3 cannot be subtracted from 0 hence we borrowed 1 from the 9 in the tenths place. Now in the hundredths place 3 is subtracted from 10 to get 7. Moreover, now in the tenths place 2 is subtracted from 8 to get 6. There is no need of borrowing in the integral part. In the hundredths place 0 subtracted from 4 is 4. In tens place 0 subtracted from 8 is 8 and in the hundreds place 4 subtracted from 6 is 2.

2. Subtract 854.87 from 990.97

Solution:

                       8  10

                 9  9   0  .  9  7

             -     8  5   4  .  8  7

                   1  3   6  .  1   0

In this subtraction there is no need of borrowing in the fractional part and hence 7 subtracted from 7 is 0 in the hundredths place and then 8 subtracted from 9 is 1 in the tenths place. In the units place 4 cannot be subtracted from 0 and hence need to borrow 1 from tens place to make it 10. Now 4 subtracted from 10 is 6.  We have borrowed 1 from 9 in the tens place. So, now we have to subtract 5 from in the tens place to get 3 and finally in the hundreds place 8 subtracted from 9 is 1.

5th Grade Math

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