Adding Decimals

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

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.

example

Add: [latex]23.5+41.38[/latex]

Show Solution

Solution

	[latex]23.5+41.38[/latex]
Write the numbers vertically so the decimal points line up.
Place [latex]0[/latex] as a place holder after the [latex]5[/latex] in [latex]23.5[/latex], 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.

In the following video we show another example of how to add decimals.

Subtracting decimals

example

How much change would you get if you handed the cashier a [latex]$20[/latex] bill for a [latex]$14.65[/latex] purchase? We will show the steps to calculate this in the next example.

Subtract: [latex]20 - 14.65[/latex]

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Solution

	[latex]20 - 14.65[/latex]
Write the numbers vertically so the decimal points line up. Remember [latex]20[/latex] is a whole number, so place the decimal point after the [latex]0[/latex].
Place two zeros after the decimal point in [latex]20[/latex], 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: [latex]2.51 - 7.4[/latex]

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Solution
If we subtract [latex]7.4[/latex] from [latex]2.51[/latex], the answer will be negative since [latex]7.4>2.51[/latex]. To subtract easily, we can subtract [latex]2.51[/latex] from [latex]7.4[/latex]. Then we will place the negative sign in the result.

	[latex]2.51 - 7.4[/latex]
Write the numbers vertically so the decimal points line up.
Place zero after the [latex]4[/latex] in [latex]7.4[/latex] 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 [latex]2.51 - 7.4[/latex] so the answer is negative	[latex]2.51 - 7.4=-4.89[/latex]

This video shows another example of how to subtract one decimal from another.