Math Core

You run 1.6 kilometers on Monday and 2.75 kilometers on Tuesday. How far did you run in all? Decimals show up in distances, money and measurements all the time. The good news: you add and subtract them the same way you add and subtract whole numbers. You just have to keep each digit in the right place.

Line up the places

When you add whole numbers, you add ones to ones and tens to tens. Decimals work the same way. You add tenths to tenths and hundredths to hundredths.

The easy way to make sure the places match is to line up the decimal points. Then every digit sits above a digit with the same place value.

You can see a small sum on a number line. To find $1.2 + 0.5$ , start at 1.2 and hop forward 5 tenths:

Start at 1.2 and hop 5 tenths to land on 1.7.

So $1.2 + 0.5 = 1.7$ .

Adding and subtracting decimals

Write the numbers in a column with the decimal points lined up.
Fill empty places with zeros if it helps, so both numbers have the same number of digits after the point.
Add or subtract just like whole numbers, regrouping when you need to.
Bring the decimal point straight down into the answer.

Zeros are placeholders

Writing a zero at the end of a decimal does not change its value. $1.6$ and $1.60$ are the same amount: 6 tenths is the same as 60 hundredths. A whole number has a decimal point at its end, so $5 = 5.0 = 5.00$ .

Adding zeros makes the columns even, which makes the work easier to read.

Worked example: Adding with regrouping

Find $2.47 + 3.6$ .

Line up the decimal points and write $3.6$ as $3.60$ :

\begin{array}{r} 2.47 \\ +\,3.60 \\ \hline 6.07 \end{array}

Hundredths: $7 + 0 = 7$ .
Tenths: $4 + 6 = 10$ tenths. Write 0 and regroup 1 one.
Ones: $2 + 3 + 1 = 6$ .

So $2.47 + 3.6 = 6.07$ .

Worked example: Subtracting from a whole number

Find $5 - 2.38$ .

Write $5$ as $5.00$ so both numbers have hundredths:

\begin{array}{r} 5.00 \\ -\,2.38 \\ \hline 2.62 \end{array}

There are no hundredths or tenths to take from, so regroup: 5 ones becomes 4 ones, 9 tenths and 10 hundredths.

Hundredths: $10 - 8 = 2$ .
Tenths: $9 - 3 = 6$ .
Ones: $4 - 2 = 2$ .

So $5 - 2.38 = 2.62$ . Check by adding: $2.62 + 2.38 = 5.00$ .

Common mistake

Don't line up the last digits on the right, the way you do with whole numbers. For $4.5 + 1.25$ , lining up the right edges would put the 5 tenths on top of the 5 hundredths, and adding those makes no sense. Line up the decimal points instead: $4.50 + 1.25 = 5.75$ .

Estimate first

Before you work out the exact answer, round to whole numbers and estimate. The estimate tells you whether your decimal point ended up in a sensible spot.

Worked example: Estimate, then solve

A jar holds 12.8 liters of water. Kofi pours out 4.95 liters. How much water is left?

Estimate: $13 - 5 = 8$ , so the answer should be close to 8 liters.

Solve: Write $12.8$ as $12.80$ and subtract:

\begin{array}{r} 12.80 \\ -\,4.95 \\ \hline 7.85 \end{array}

There are 7.85 liters left. That is close to the estimate of 8, so the answer makes sense.

Tip

Money is a decimal with hundredths. $3.50 means 3 dollars and 50 cents, or 3 and 50 hundredths of a dollar. Adding prices is just adding decimals.

Practice

Practice 1

Find $0.4 + 0.5$ .

Type a number.

Practice 2

Find $3.25 + 1.6$ .

Type a number.

Practice 3

Find $8.7 - 2.35$ .

Type a number.

Practice 4

Find $6 - 1.48$ .

Type a number.

Practice 5

Leo says $5.3 + 2.45 = 2.98$ . What is the correct sum?

Practice 6

Maya buys a notebook for $4.75 and a pack of pens for $2.60. She pays with a $10 bill. How much change does she get, in dollars?

Type a number.

Practice 7

Find $15.08 - 7.9$ .

Type a number.

Practice 8

A garden needs 6 centimeters of rain this week. It rains 1.25 cm on Monday, 0.8 cm on Wednesday and 2.4 cm on Friday. How many more centimeters of rain does the garden need?

Type a number.