To subtract decimal numbers:
- Put the numbers in a vertical column aligning the decimal points.
- Subtract each column, starting on the right and working left. ...
- Place the decimal point in the answer directly below the decimal points in the terms.
- Check the answer by adding.
When asked to add or subtract decimals, the most important step is to line up the decimal points.
Adding:
Ex.1) 13.6 + 17.8
Step 1: Line up the decimal points so that similar place values are lined up. In other words, the tens place in both numbers should be lined up, the ones place in both numbers should be lined up, etc.
Step 2: Add the digits together that are lined up.
Ex. 2) 14.86 + 22.9
If the numbers do not have the same number of digits after the decimal point, you can use "filler zeros" to help you line up the numbers.
Ex 3.) 45 + 6.98
A common mistake that is often made is that the 45 is added to the 98. However, here the 45 represents a whole number. It is 4 tens and 5 ones. The 98 represents 9 tenths and 8 hundredths. These numbers do not hold the same place values.
So instead, we can add a decimal point at the end of the 45 and then add two filler zeros so that the numbers can be lined up.
45.00 + 6.98
Now we are ready to solve:
Subtracting:
The steps for subtracting numbers with decimals are exactly the same as adding decimals. Let's take a look at a couple of examples.
Ex. 4) 239.83 - 125.51
First we will line up the numbers by making sure the decimals are lined up. Then we just subtract the numbers that are in common place value positions.
Ex. 5) 98.3 - 45.67
We will start by lining them up.
In the subtraction examples, the filler zeros are even more helpful. Some make the mistake of placing a 7 in the hundredths place of the answer. However, take a look at what happens with the filler zero.
With the zero here, we can see that we need to borrow in order to subtract.
Ex. 6) 34 - 32.87
Like example 3, in the adding section, we need to give this whole number a decimal and some filler zeros.
Now, we can see that we are not subtracting the 34 and 87. Instead, we are subtracting a number in the tens place with another number in the tens place. We need to be sure to add or subtract the values that are in the same place value.
So the steps to adding and subtracting are this:
Adding:
Ex.1) 13.6 + 17.8
Step 1: Line up the decimal points so that similar place values are lined up. In other words, the tens place in both numbers should be lined up, the ones place in both numbers should be lined up, etc.
Step 2: Add the digits together that are lined up.
Ex. 2) 14.86 + 22.9
If the numbers do not have the same number of digits after the decimal point, you can use "filler zeros" to help you line up the numbers.
Ex 3.) 45 + 6.98
A common mistake that is often made is that the 45 is added to the 98. However, here the 45 represents a whole number. It is 4 tens and 5 ones. The 98 represents 9 tenths and 8 hundredths. These numbers do not hold the same place values.
So instead, we can add a decimal point at the end of the 45 and then add two filler zeros so that the numbers can be lined up.
45.00 + 6.98
Now we are ready to solve:
Subtracting:
The steps for subtracting numbers with decimals are exactly the same as adding decimals. Let's take a look at a couple of examples.
Ex. 4) 239.83 - 125.51
First we will line up the numbers by making sure the decimals are lined up. Then we just subtract the numbers that are in common place value positions.
Ex. 5) 98.3 - 45.67
We will start by lining them up.
In the subtraction examples, the filler zeros are even more helpful. Some make the mistake of placing a 7 in the hundredths place of the answer. However, take a look at what happens with the filler zero.
With the zero here, we can see that we need to borrow in order to subtract.Ex. 6) 34 - 32.87
Like example 3, in the adding section, we need to give this whole number a decimal and some filler zeros.
Now, we can see that we are not subtracting the 34 and 87. Instead, we are subtracting a number in the tens place with another number in the tens place. We need to be sure to add or subtract the values that are in the same place value.
So the steps to adding and subtracting are this:
1.) Line up the place values of the numbers by lining up the decimals.
2.) Add in filler zeros if needed.
3.) Add or Subtract the numbers in the same place value positions.
2.) Add in filler zeros if needed.
3.) Add or Subtract the numbers in the same place value positions.
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