Adding and Subtracting Decimals

 

Learning Objective(s)

·         Add two or more decimals.

·         Subtract two or more decimals, with and without regrouping.

·         Solve application problems that require decimal addition or subtraction.

 

 

Since dollars and cents are typically written as decimals, you often need to work with decimals. Knowing how to add and subtract decimal numbers is essential when you deposit money to (and withdraw money from) your bank account; perform an incorrect calculation, and you may be costing yourself some cash!

 

When adding or subtracting decimals, it is essential that you pay attention to the place value of the digits in the numbers you are adding or subtracting. This will be the key idea in the discussion that follows. Let’s begin with an everyday example that illustrates this idea before moving into more general techniques.

 

 

Suppose Celia needs $0.80 to ride the bus from home to her office. She reaches into her purse and pulls out the following coins: 3 quarters, 1 dime and 2 pennies. Does she have enough money to ride the bus?

 

Take a moment to think about this problem. Does she have enough money? Some people may solve it like this: “I know each quarter is 25¢, so three quarters is 75¢. Adding a dime brings me to 85¢, and then another two pennies is 87¢. So, Celia does have enough money to ride the bus.”

 

This problem provides a good starting point for our conversation because you can use your knowledge about pocket change to understand the basics about how to add decimals. The coins you use every day can all be represented as whole cent values, as shown above. But they can also be represented as decimal numbers, too, because quarters, dimes, nickels and pennies are each worth less than one whole dollar.

 

 

 

Celia has 87¢. You can also write this amount in terms of the number of dollars she has: $0.87. The table below shows a step-by-step approach to adding the coins in terms of cents and also as dollars. As you review the table, pay attention to the place values.

 

 

When you add whole numbers, as shown in the Value (cents) column above, you line up the numbers so that the digits in the ones place-value column are aligned.

 

In order to keep the numbers in the proper place-value column when adding decimals, align the decimal points. This will keep the numbers aligned; ones to ones, tenths to tenths, hundredths to hundredths, and so on. Look at the column titled Value (dollars). You will see that place value is maintained, and that the decimal points align from top to bottom.

 

Adding Decimals   To add decimals: ·         Align the decimal points, which will allow all the digits to be aligned according to their place values. ·         Add just as you would add whole numbers, beginning on the right and progressing to the left. ·         Write the decimal point in the sum, aligned with the decimal points in the numbers being added.

 

 

 

 

 

Add: 0.08 + 0.156   A) 0.956   B) 0.236   C) 0.164   D) 0.1568   Show/Hide Answer A) 0.956 Incorrect. Pay attention to the locations of the decimal points. An answer of 0.956 would have been correct for the problem 0.8 + 0.156. The correct answer is 0.236.   B) 0.236 Correct. Line up the decimal points and then add. The correct answer is 0.236.   C) 0.164 Incorrect. Pay attention to the locations of the decimal points. An answer of 0.164 would have been correct for the problem 0.008 + 0.156. You can only add zeros at the end of the number. The correct answer is 0.236.   D) 0.1568 Incorrect. Pay attention to the locations of the decimal points. An answer of 0.1568 would have been correct for the problem 0.0008 + 0.156. You can only add zeros at the end of the number. The correct answer is 0.236.

 

 

 

Subtracting decimals uses the same setup as adding decimals: line up the decimal points, and then subtract.

 

In cases where you are subtracting two decimals that extend to different place values, it often makes sense to add extra zeros to make the two numbers line up—this makes the subtraction a bit easier to follow.

 

 

Subtracting Decimals   To subtract decimals: ·         Align the decimal points, which will allow all of the digits to be aligned according to their place values. ·         Subtract just as you would subtract whole numbers, beginning on the right and progressing to the left. ·         Align the decimal point in the difference directly below the decimal points in the numbers that were subtracted.

 

 

 

Subtract. 43.21 – 8.1   A) 35.11   B) 42.40   C) 37.79   D) 35.2   Show/Hide Answer A) 35.11 Correct. Line up the two numbers so that the decimal points are aligned, and then subtract. The difference is 35.11.   B) 42.40 Incorrect. Pay attention to the location of the decimal point. An answer of 42.40 would have been correct for the problem 43.21 – 0.81. The correct answer is 35.11.   C) 37.79 Incorrect. To subtract, you need to align the decimal points first. The correct answer is 35.11.   D) 35.2 Incorrect. Pay attention to the location of the decimal point. An answer of 35.2 would have been correct for the problem 43.21 – 8.01. The correct answer is 35.11.

 

 

 

In adding and subtracting decimals, you may have noticed that as long as you line up the decimal points in the numbers you are adding or subtracting, you can operate upon them as you would whole numbers.

 

Determining whether you need to add or subtract in a given situation is also straightforward. If two quantities are being combined, then add them. If one is being withdrawn from the other, then subtract them.

 

 

 

Helene ran the 100-meter dash twice on Saturday. The difference between her two times was 0.3 seconds. Which pair of numbers below could have been her individual race times?   A) 14.22 and 14.25 seconds   B) 14.22 and 17.22 seconds   C) 14.22 and 14.58 seconds   D) 14.22 and 13.92 seconds   Show/Hide Answer A) 14.22 and 14.25 seconds Incorrect. The difference between these times is 0.03 seconds, not 0.3 seconds. The correct answer is 14.22 and 13.92 seconds.   B) 14.22 and 17.22 seconds Incorrect. The difference between these times is 3 seconds, not 0.3 seconds. The correct answer is 14.22 and 13.92 seconds.   C) 14.22 and 14.58 seconds Incorrect. The difference between these times is 0.36 seconds, not 0.3 seconds. The correct answer is 14.22 and 13.92 seconds.   D) 14.22 and 13.92 seconds Correct. 14.22 – 13.92 = 0.3; the difference between Helene’s two race times is 0.3 seconds.

 

 

 

When adding or subtracting decimals, you must always align the decimal points, which will allow the place-value positions to fall in place. Then add or subtract as you do with whole numbers, regrouping as necessary. You can use these operations to solve real-world problems involving decimals, especially those with money.