Introduction

Let's compute the following sum:

4,745,136 + 25,985

We proceed, as usual, using the standard algorithm.

First, we line up our numbers:

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

Then, we add the numbers in each place value (from right to left):

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

Therefore, 4,745,136 + 25,985 = 4,771,121.

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Example: Adding Numbers Up to Seven Digits Without Carrying

Calculate the sum 5,326,143 + 271,612.

EXPLANATION

First, we line up our numbers:

\begin{array}{cccccccc} & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \end{array}

Next, we proceed by adding the numbers in each place value (from right to left):

\begin{array}{cccccccc} & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 3 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & & \!\!\!\! 2 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 2 \!\!\!\! \\ \hline & & \!\!\!\! 5 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 9 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 5 \!\!\!\!& \!\!\!\! 5 \!\!\!\! \end{array}

Therefore, 5,326,143 + 271,612 = 5,597,755.

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Practice: Adding Numbers Up to Seven Digits Without Carrying

$841,231 + 2,643=$

a
 $1,043,874$
b
 $953,874$
c
 $843,874$
d
 $923,874$
e
 $1,943,874$
Practice: Adding Numbers Up to Seven Digits Without Carrying

$5,034 + 602,915=$

a
 $652,949$
b
 $607,949$
c
 $657,949$
d
 $1,107,949$
e
 $602,949$
Example: Adding Numbers Up to Seven Digits With Carrying

What is 3,246,341+ 71,769?

EXPLANATION

First, we line up our numbers:

\begin{array}{cccccccc} & & \!\!\!\! 3 \!\!\!\!& \!\!\!\! 2 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 3 \!\!\!\!& \!\!\!\! 4 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & & & \!\!\!\! 7 \!\!\!\!& \!\!\!\! 1 \!\!\!\!& \!\!\!\! 7 \!\!\!\!& \!\!\!\! 6 \!\!\!\!& \!\!\!\! 9 \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\!& \!\!\!\! \!\!\!\! \end{array}

Next, we proceed by adding the numbers in each place value (from right to left):

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

Therefore, 3,246,341+ 71,769 = 3,318,110.

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Practice: Adding Numbers Up to Seven Digits With Carrying

$5,326,148 + 2,148,938 =$

a
 $7,274,086$
b
 $7,475,086$
c
 $7,535,086$
d
 $7,325,086$
e
 $7,415,086$
Practice: Adding Numbers Up to Seven Digits With Carrying

$6,140 + 9,998,360 =$

a
b
c
d
e
Example: Adding Numbers Up to Seven Digits: Word Problems

In 2020 , a certain country had an elderly population of 2,079,439 and a non-elderly population of 8,019,826. What was the total population of the country?

EXPLANATION

To find the total population of the country, we need to calculate the value of

2,079,439 + 8,019,826.

First, we line up our numbers:

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

Next, we proceed by adding the numbers in each place value (from right to left):

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

So, 2,079,439 + 8,019,826 = 10,099,265.

Therefore, the total population of the country was 10,099,265.

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Practice: Adding Numbers Up to Seven Digits: Word Problems

The child population of a particular city is $1,352,997.$ The adult population of the city is $1,627,002.$ What is the total population of the city?

a
 $2,979,999$
b
 $3,978,899$
c
 $3,079,999$
d
 $2,869,899$
e
 $2,968,999$
Practice: Adding Numbers Up to Seven Digits: Word Problems

According to a center for disease control in the United States, the number of hospitalizations due to the flu was $379,950$ in $2019$ and $389,870$ in $2020.$ How many hospitalizations due to the flu were there during both years combined?

a
 $769,820$
b
 $770,920$
c
 $659,820$
d
 $669,920$
e
 $750,820$
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