Introduction

Adding decimals is no harder than adding whole numbers.

For example, let's find 0.4 + 2.6.

First, we write one number above the other, lining up the decimal points and placing a decimal point below the others in our answer:

\begin{array}{cccccccc} & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\ \hline & & & \!\!\!\! . \!\!\!\!& \end{array}

Next, we proceed by adding the two numbers just as we would with whole numbers. After each addition, we write the ones place and carry the tens place of the result.

\begin{array}{cccccccc} & & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& \\ & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\ \hline & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 0 \!\!\!\! \end{array}

Therefore, 0.4 + 2.6 = 3.

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Example: Adding Two-Digit and Three-Digit Decimals

What is 0.94 + 8.32?

EXPLANATION

First, we line up the decimal points:

\begin{array}{cccccccc} & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & & & \!\!\!\! . \!\!\!\!& & \end{array}

Next, we proceed by adding the two numbers just as we would with whole numbers:

\begin{array}{cccccccc} & & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\ & & \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 8 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \end{array}

Therefore, 0.94 + 8.32 = 9.26.

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Practice: Adding Two-Digit and Three-Digit Decimals

$1.1+2.2 =$

a
 $3.3$
b
 $3.6$
c
 $3.4$
d
 $3.1$
e
 $3.2$
Practice: Adding Two-Digit and Three-Digit Decimals

$2.16+4.71 =$

a
 $4.87$
b
 $6.76$
c
 $4.76$
d
 $8.87$
e
 $6.87$
Example: Adding Decimals Containing Different Numbers of Whole Digits

What is 2.43 + 50.41?

EXPLANATION

First, we line up the decimal points:

\begin{array}{cccccccc} & & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\ \hline & & & & \!\!\!\! . \!\!\!\!& & \end{array}

Next, we proceed by adding the two numbers just as we would with whole numbers:

\begin{array}{cccccccc} & & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\ \hline & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \end{array}

Therefore, 2.43 + 50.41 = 52.84.

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Practice: Adding Decimals Containing Different Numbers of Whole Digits

$4.95 + 79.22 =$

a
 $84.28$
b
 $84.17$
c
 $85.33$
d
 $84.47$
e
 $83.12$
Practice: Adding Decimals Containing Different Numbers of Whole Digits

$7.92 +412.34 =$

a
 $419.24$
b
 $419.46$
c
 $420.18$
d
 $420.26$
e
 $420.98$
Example: Adding Four-Digit, Five-Digit and Six-Digit Decimals

What is 982.97 + 306.74?

EXPLANATION

First, we line up the decimal points:

\begin{array}{cccccccc} & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \hline & & & & & \!\!\!\! . \!\!\!\!& & \end{array}

Next, we proceed by adding the two numbers just as we would with whole numbers:

\begin{array}{cccccccc} & & & & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\! \\ & & \!\!\!\! 9 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \end{array}

Therefore, 1,289.71.

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Practice: Adding Four-Digit, Five-Digit and Six-Digit Decimals

$8.135 + 7.901 =$

a
 $16.046$
b
 $16.136$
c
 $17.036$
d
 $16.036$
e
 $15.036$
Practice: Adding Four-Digit, Five-Digit and Six-Digit Decimals

$72.112 + 52.303 =$

a
 $125.415$
b
 $124.315$
c
 $124.425$
d
 $124.515$
e
 $124.415$
Example: Word Problems

Brandon stirs 4.76 liters of milk with 2.82 liters of water in a pot. How much liquid is in the pot?

EXPLANATION

To find how much liquid is in the pot, we need to calculate 4.76 + 2.82.

First, we line up the decimal points:

\begin{array}{cccccccc} & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & & & \!\!\!\! . \!\!\!\!& & \end{array}

Next, we proceed by adding the two numbers just as we would with whole numbers:

\begin{array}{cccccccc} & & \!\!\!\! \color{blue}\substack{ \\ 1 } \!\!\!\!& & \\ & & \!\!\!\! 4 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! . \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \end{array}

Therefore, there are 7.58 liters of liquid in the pot.

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Practice: Word Problems

Emmy spent $\$1.91$ on fruits and $\$2.29$ on vegetables in a grocery store. How much money did Emmy spend in total?

a
 $\$3.20$
b
 $\$4.20$
c
 $\$4.10$
d
 $\$3.19$
e
 $\$3.10$
Practice: Word Problems

Martha downloaded two apps for her smartphone. One was $21.54 \, \textrm{mb}$ and the other was $24.05 \, \textrm{mb}.$ What size was the combined download?

a
 $47.46 \, \textrm{mb}$
b
 $50.54 \, \textrm{mb}$
c
 $56.54 \, \textrm{mb}$
d
 $48.45 \, \textrm{mb}$
e
 $45.59 \, \textrm{mb}$
Practice: Word Problems

If Jane has $\$8.75$ in her purse and $\$ 264.45$ in her bank account, how much money does she have in total?

a
 $251.25$ dollars
b
 $262.40$ dollars
c
 $233.70$ dollars
d
 $211.30$ dollars
e
 $273.20$ dollars
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