Subtracting decimals

Subtracting decimals is very similar to subtracting whole numbers. However you must remember that when subtracting decimals, you must line up the decimal points vertically. This means that if you are subtracting one decimal from another, you must write them so that the decimal point of the second number is directly under the decimal point of the first. Look at the examples below.

Example 1

17.98 – 5.75

Step 1: Make sure that the decimal points are lined up vertically as shown below.

Step 2: Subtract as you normally would with whole numbers. However you must remember that the decimal point in your answer must be placed directly under the other decimal points. Look at the working below.

Example 2 

What is the difference between 25.81 and 13.5?

Step 1: Line up the decimal points vertically as shown below. This may look a bit strange as one of the numbers has no digit in the hundredths place. However this is correct as the decimal points are lined up vertically.

Step 2: Subtract as you normally would. Note that you can add a zero in the hundredths column as shown below. This does not change the value of the number (13.5 = 13.50).

Example 3 (Subtracting decimals with regrouping)

98.35 – 45.61

Step 1: Make sure the decimal points are lined up vertically as shown below.

Step 2: Subtract as you normally would. Notice that in the tenths column, we cannot subtract 6 from 3. We need to regroup. Look at the working below.

Since we cannot subtract 6 from 3, we must borrow from the next column (ones column). We know that one is equal to ten tenths (1 = 10/10). Therefore, when we add ten tenths to three tenths we get thirteen tenths (13/10). We can then subtract 6 tenths from 13 tenths. This is just like what we do when subtracting whole numbers.

Example 4 (Subtracting a decimal from a whole number)

17 – 4.08

Step 1: Write 17 as a decimal by adding a decimal point and zeros. In this case 17 can be write as 17.oo. Ensure that the decimal points are lined up vertically as shown below.

Step 2: Subtract as you normally would. This example involves regrouping as well. Notice that in the hundredths column, we cannot subtract 8 from 0. Look at the working below.

Notice that we cannot borrow from the tenths column as there is another zero in the tenths place. We borrow one from the ones column and bring it over to the tenths column. Remember that one equals ten tenths. However we now need to borrow one tenth to bring over to the hundredths column. This leaves nine tenths in the tenths column. In the hundredths column, the one tenth we borrowed is equal to ten hundredths. Now we can subtract without any issues.