Introduction

Using the standard algorithm, we can calculate the sum of two numbers containing any number of digits.

Let's use the standard algorithm to compute the following sum:

32,810+8,921

The procedure is the same as the one we've seen before. We start by lining up our numbers:

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

Therefore, 32,810+8,921 = 41,731.

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Example: Adding Numbers Up to Five Digits

What is 23,861+5,026?

EXPLANATION

First, we line up our numbers:

\begin{array}{cccccccc} & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 6 \!\!\!\!& \!\!\!\! 1 \!\!\!\! \\ \!\!\!\!+\!\!\!\! & & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \hline & & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! & \!\!\!\! \!\!\!\! \end{array}

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

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

Therefore, 23,861+5,026 = 28,887.

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Practice: Adding Numbers Up to Five Digits

$23,846+4,123 =$

a
 $29,697$
b
 $27,996$
c
 $26,979$
d
 $27,969$
e
 $29,796$
Practice: Adding Numbers Up to Five Digits

$1,241+4,217 =$

a
 $5,458$
b
 $5,447$
c
 $5,448$
d
 $5,455$
e
 $5,558$
Example: Adding Numbers Up to Five Digits With Carrying

Compute the value of 89,743+32,876.

EXPLANATION

First, we line up our numbers:

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

Therefore, 89,723+32,876 = 122,619.

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Practice: Adding Numbers Up to Five Digits With Carrying

$20,129+9,028=$

a
 $28,167$
b
 $29,257$
c
 $29,267$
d
 $28,157$
e
 $29,157$
Practice: Adding Numbers Up to Five Digits With Carrying

$42,732+6,598=$

a
 $48,030$
b
 $48,230$
c
 $49,330$
d
 $49,331$
e
 $48,329$
Example: Adding Numbers Up to Five Digits: Word Problems

Mike wrote two essays. There are 11,391 words in the first essay and 7,942 words in the second essay. How many words did Mike write altogether?

EXPLANATION

To find how many words Mike wrote altogether, we need to calculate the value of

11,391 + 7,942.

First, we line up our numbers:

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

So, 11,391 + 7,942 = 19,333.

Therefore, Mike wrote 19,333 words in total.

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Practice: Adding Numbers Up to Five Digits: Word Problems

A household used $14,340$ liters of water during September and $9,875$ liters in October. How many liters of water did the household use during these two months?

a
 $14,215$ liters
b
 $24,115$ liters
c
 $23,215$ liters
d
 $24,215$ liters
e
 $23,115$ liters
Practice: Adding Numbers Up to Five Digits: Word Problems

A supermarket sold $91,157$ red apples and $72,865$ green apples in July. How many apples did the supermarket sell in total?

a
 $163,022$
b
 $164,022$
c
 $164,912$
d
 $164,812$
e
 $94,022$
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