Operations with Decimals

Adding and Subtracting Decimals

Adding and Subtracting decimals is very similar to adding and subtracting whole numbers, the only difference is that we have a decimal point!

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When adding and subtracting decimals it is important that we always line up the decimals according to their place value. We can do that by placing the decimal points on top of each other.

Step by Step

To add decimals, follow these steps:

1. Write down the numbers, one under the other, with the decimal points lined up

2. Put in zeros so the numbers have the same length

2. Then add normally, remembering to put the decimal point in the answer

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Example 1: Adding Decimals Example :

3.4 + 0.17

Step 1: Let’s first line the decimals points and write down the numbers according to their place values under the other.

3 . 4 0 - we can add a zero to make them equal length

+ 0 . 1 7

Step 2 : We add the hundredths, followed by the tenths and then the ones

3 . 4 0 - we can add a zero to make them equal length

+ 0 . 1 7

3 . 5 7 - make sure the decimal point is written in your answer

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Example 2: Subtracting Decimals

3.4 - 0.17

Step 1: Lets first line the decimals points and write down the numbers according to their place values under the other.

3 . 4 0 - we can add a zero to make them equal length

- 0 . 1 7

Step 2 : We subtract the hundredths, followed by the tenths and then the ones

3 . 4 0 - we can add a zero to make them equal length

- 0 . 1 7 - we borrow a 1 from the 4, so we subtract (10-7)

3 . 2 3 - make sure the decimal point is written in your answer

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Multiplying Decimals

Step by Step

Steps to follow when multiplying with whole numbers

1. Multiply normally, ignoring the decimal point

2. Put the decimal point back into the answer- it will have as many decimal places as the two original numbers combined had.

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Example - 2.734 x 18

Step 1: Multiply normally, ignoring the decimal points:

2 7 3 4

x 1 8

21872

+ 2734

49212

Step 2 : Put the decimal point back into the answer by counting the total number of decimal places

2.734 - Has three decimal places

18 - Has none

49 212 - We count three decimal places to the left

Therefore our answer is 49.212

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Example - 2.78 x 0.6

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Step 1: Multiply normally, ignoring the decimal points:

2 7 8

x 6

1668

Step 2 : Put the decimal point back into the answer by counting the total number of decimal places

2.78 - Has two decimal places

0.6 - Has one

16 68 - We count three decimal places to the left

Therefore our answer is 1.668

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Dividing Decimals by Decimals

Dividing Decimals by Decimals

Step 1: Turn the divisor (the number you’re dividing by) into a whole number by moving the decimal point all the way to the right; at the same time, move the decimal point in the dividend (the number you’re dividing) the same number of places to the right.

For example, suppose you want to divide 10.274 by 0.11. Write the problem as usual:

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Step 2: Turn 0.11 into a whole number by moving the decimal point in 0.11 two places to the right, giving you 11. At the same time, move the decimal point in 10.274 two places to the right, giving you 1,027.4:

Dividing Decimals by Decimals

Step 3: Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.

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Step 4: Divide as usual

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Dividing Decimals by Decimals

11 goes into 37 three times. The important thing is to place the next digit in the answer just above the 7:

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Bring down the next number, 4. Now, 11 goes into 44 four times. Again, be careful to place the next digit in the quotient just above the 4, and complete the division:

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