Introduction

We can use the standard algorithm to add multiple multi-digit whole numbers.

For example, let's use the standard algorithm to compute the following sum:

801 + 523 + 198

First, we line up our numbers:

\begin{array}{cccccccc} & & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \end{array}

Next, we add the numbers in each place value (from right to left). However, this time, we need to sum three numbers in each place value, as well as any carried digits:

\begin{array}{cccccccc} & \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \!\!\!\! \\ & & \!\!\!\! 8 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \\ \hline & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \end{array}

Therefore, 801 + 523 + 198 = 1,522.

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Example: Adding Three Numbers Up to Three Digits

Lauren is listening to some songs while waiting for a train. The duration of the first song is 123 seconds, the second is 182 seconds, and the third is 157 seconds. What is the total duration of all three songs?

EXPLANATION

To find the total duration of all three tracks, we need to compute the sum

123 + 182 + 157.

First, we line up our numbers:

\begin{array}{cccccccc} & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \end{array}

Next, we proceed by adding the numbers using the standard algorithm: \begin{array}{cccccccc} & \!\!\!\! \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \!\!\!\! \\ & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \end{array}

So, we have

123 + 182 + 157 = 462.

Therefore, the total duration of all three songs is 462 seconds.

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Practice: Adding Three Numbers Up to Three Digits

$31 + 457 + 99 =$

a
 $577$
b
 $556$
c
 $587$
d
 $487$
e
 $477$
Practice: Adding Three Numbers Up to Three Digits

$425 + 69 + 278 =$

a
 $662$
b
 $772$
c
 $672$
d
 $762$
e
 $771$
Example: Adding Three Numbers Up to Five Digits

What is 31,252 + 12,892 + 25,034?

EXPLANATION

First, we line up our numbers:

\begin{array}{cccccccc} & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \end{array}

Next, we proceed by adding the numbers using the standard algorithm:

\begin{array}{cccccccc} & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \\ & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\! \end{array}

Therefore,

31,252 + 12,892 + 25,034= 69,178.

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Practice: Adding Three Numbers Up to Five Digits

$9,375 + 15,761+62,791 =$

a
 $77,927$
b
 $87,727$
c
 $87,827$
d
 $87,927$
e
 $86,927$
Practice: Adding Three Numbers Up to Five Digits

In a particular year, Dan drove $13,589 \,\text{mi},$ Brian drove $12,825\,\text{mi},$ and Faby drove $14,029\,\text{mi}.$ How many miles did they drive in total?

a
 $41,433 \,\text{mi}$
b
 $40,443 \,\text{mi}$
c
 $30,343 \,\text{mi}$
d
 $31,443 \,\text{mi}$
e
 $41,423 \,\text{mi}$
Example: Adding Three Numbers Up to Seven Digits

2,078,503 + 148,450 + 1,885,047 =

EXPLANATION

First, we line up our numbers:

\begin{array}{cccccccc} & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \end{array}

Next, we proceed by adding the numbers using the standard algorithm:

\begin{array}{cccccccc} & \!\!\!\! \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 2 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 2 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \small{ \color{blue} 1 } \!\!\!\!& \!\!\!\! \!\!\!\! \\ & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 1 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 8 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\!& \!\!\!\! 0 \!\!\!\! \end{array} Therefore,

2,078,503 + 148,450 + 1,885,047 = 4,112,000.

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Practice: Adding Three Numbers Up to Seven Digits

$3,592,009 + 267,457 + 2,405,812 =$

a
 $6,265,278$
b
 $5,255,278$
c
 $6,264,268$
d
 $6,365,288$
e
 $5,265,268$
Practice: Adding Three Numbers Up to Seven Digits

The area of the USA is $3,796,742\,\textrm{mi}^2,$ the area of Canada is $3,855,100\,\textrm{mi}^2,$ and the area of Mexico is $761,610\,\textrm{mi}^2.$ What is the total area of these three countries?

a
 $6,403,452\,\textrm{mi}^2$
b
 $8,413,452\,\textrm{mi}^2$
c
 $7,413,452\,\textrm{mi}^2$
d
 $7,213,452\,\textrm{mi}^2$
e
 $8,312,452\,\textrm{mi}^2$
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