Decimal Operations

Let's take one more look at the lunch order from the start of Decimals, this time noticing how the numbers were

$\begin{aligned} \$ 3.45 & \qquad \text { Sandwich } \\ \$ 1.25 & \qquad\text { Water } \\ +\$ 0.33 & \qquad\text { Tax } \\ \overline{\$5.03} & \qquad \text { Total } \end{aligned}$

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.

Step 1. Write the numbers vertically so the decimal points line up.

Step 2. Use zeros as place holders, as needed.

Step 3. 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.

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

Source: Rice University, https://openstax.org/books/prealgebra/pages/5-2-decimal-operations
This work is licensed under a Creative Commons Attribution 4.0 License.

EXAMPLE 5.11

Add: $3.7+12.4$.

EXAMPLE 5.12

Add: $23.5+41.38$.

EXAMPLE 5.13

Subtract: $20-14.65$.

EXAMPLE 5.14

Subtract: $2.51-7.4$.

EXAMPLE 5.11

Solution

EXAMPLE 5.12

Solution

EXAMPLE 5.13

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 $0$.	$\begin{array}{r}20. \quad \\- 14.65 \\\hline\end{array}$
Place two zeros after the decimal point in $20$, as place holders so that both numbers have two decimal places.	$\begin{array}{r}20.\color{red}{00} \\-14.65 \\\hline\end{array}$
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 5.14

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.