Adding and Subtracting Decimals

Let’s take one more look at the lunch order from the start of the previous topic, this time noticing how the numbers were added together.

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

All three items (sandwich, water, tax) were priced in dollars and cents, so we lined up the dollars under the dollars and the cents under the cents, with the decimal points lined up between them. Then we just added each column, as if we were adding whole numbers. By lining up decimals this way, we can add or subtract the corresponding place values just as we did with whole numbers.

How to Add or subtract decimals.

Write the numbers vertically so the decimal points line up.
Use zeros as place holders, as needed.
Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Example

Add: $3.7+12.4.$

Solution

	$3.7+12.4$
Write the numbers vertically so the decimal points line up.	$\begin{array}{r} 3.7 \\ +12.4 \\ \_\_\_\_\_ \end{array}$
Place holders are not needed since both numbers have the same number of decimal places.
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.	$\begin{array}{r} 3.7 \\ +12.4 \\ \_\_\_\_\_ \\ 16.1 \end{array}$

Example

Add: $23.5+41.38.$

Solution

	$23.5+41.38$
Write the numbers vertically so the decimal points line up.
Place 0 as a place holder after the 5 in 23.5, so that both numbers have two decimal places.
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

How much change would you get if you handed the cashier a $\text{\$20}$ bill for a $\text{\$14.65}$ purchase? We will show the steps to calculate this in the next example.

Example

Subtract: $20-14.65.$

Solution

	$20-14.65$
Write the numbers vertically so the decimal points line up. Remember 20 is a whole number, so place the decimal point after the 0.
Place two zeros after the decimal point in 20, as place holders so that both numbers have two decimal places.
Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Example

Subtract: $2.51-7.4.$

Solution

If we subtract $7.4$ from $2.51,$ the answer will be negative since $7.4>2.51.$ To subtract easily, we can subtract $2.51$ from $7.4.$ Then we will place the negative sign in the result.

	$2.51-7.4$
Write the numbers vertically so the decimal points line up.
Place zero after the 4 in 7.4 as a place holder, so that both numbers have two decimal places.
Subtract and place the decimal in the answer.
Remember that we are really subtracting $2.51-7.4$ so the answer is negative.	$2.51-7.4=-4.89$

Optional Video: Adding and Subtracting Decimals

	\(3.7+12.4\)
Write the numbers vertically so the decimal points line up.	\(\begin{array}{r} 3.7 \\ +12.4 \\ \_\_\_\_\_ \end{array}\)
Place holders are not needed since both numbers have the same number of decimal places.
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.	\(\begin{array}{r} 3.7 \\ +12.4 \\ \_\_\_\_\_ \\ 16.1 \end{array}\)

	\(23.5+41.38\)
Write the numbers vertically so the decimal points line up.
Place 0 as a place holder after the 5 in 23.5, so that both numbers have two decimal places.
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

	\(20-14.65\)
Write the numbers vertically so the decimal points line up. Remember 20 is a whole number, so place the decimal point after the 0.
Place two zeros after the decimal point in 20, as place holders so that both numbers have two decimal places.
Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

	\(2.51-7.4\)
Write the numbers vertically so the decimal points line up.
Place zero after the 4 in 7.4 as a place holder, so that both numbers have two decimal places.
Subtract and place the decimal in the answer.
Remember that we are really subtracting \(2.51-7.4\) so the answer is negative.	\(2.51-7.4=-4.89\)

Adding and Subtracting Decimals