Introduction

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

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

42,345 - 3,124

First, we line up our numbers (ones over ones, tens over tens, hundreds over hundreds, and so on):

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 4 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 3 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\! \\ \!\!\!\!-\!\!\!\! & & & \!\!\! 3 \!\!\!& \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\! \\ \hline & & \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\! \end{array}

Next, we proceed by subtracting the numbers in each place value from right to left, borrowing where needed.

\require{cancel} \begin{array}{cccccccc} & & \!\!\! \color{blue}\substack{ \\ 3 } & \!\!\!\! \color{blue}\substack{ \\ 12 } & \!\!\! & \!\!\! & \!\!\! \\ & & \!\!\!\!\! \cancel{4} \!\!\!& \!\!\!\!\! \cancel{2} \!\!\!& \!\!\! 3 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\! \\ \!\!\!\!-\!\!\!\! & & & \!\!\! 3 \!\!\!& \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\! \\ \hline & & \!\!\! 3 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 1 \!\!\! \end{array}

Therefore,

42,345 - 3,124 = 39,221.

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Example: Subtracting Numbers Up to Five Digits Without Borrowing

Compute the value of 57,458 - 25,242.

EXPLANATION

First, we line up our numbers:

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 5 \!\!\!& \!\!\! 7 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 8 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 2 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 2 \!\!\! \\ \hline & & \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\! \end{array}

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

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 5 \!\!\!& \!\!\! 7 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 8 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 2 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 2 \!\!\! \\ \hline & & \!\!\! 3 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 1 \!\!\!& \!\!\! 6 \!\!\! \end{array}

Therefore, 57,458 - 25,242 = 32,216.

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Practice: Subtracting Numbers Up to Five Digits Without Borrowing

$44,236 - 21,023 =$

a
 $23,323$
b
 $23,123$
c
 $21,321$
d
 $23,213$
e
 $22,123$
Practice: Subtracting Numbers Up to Five Digits Without Borrowing

$12,747 - 2,515 =$

a
 $9,579$
b
 $9,759$
c
 $10,252$
d
 $10,232$
e
 $10,352$
Example: Subtracting Numbers Up to Five Digits With Borrowing

What is 83,005 - 52,009?

EXPLANATION

First, we line up our numbers:

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

Next, we proceed by subtracting the numbers in each place value from right to left, borrowing where needed.

\require{cancel} \begin{array}{cccccccc} & & \!\!\! & \!\!\! \color{blue}\substack{ \\ 2 } & \!\!\! \color{blue}\substack{ \\ 9 } & \!\!\! \color{blue}\substack{ \\ 9 } & \!\!\!\! \color{blue}\substack{ \\ 15 } \\ & & \!\!\! 8 \!\!\!& \!\!\!\! \cancel{3} \!\!\!& \!\!\!\! \cancel{0} \!\!\!& \!\!\!\! \cancel{0} \!\!\!& \!\!\!\!\! \cancel{5} \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 5 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 9 \!\!\! \\ \hline & & \!\!\! 3 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 6 \!\!\! \end{array} Therefore, 83,005 - 52,009 = 30,996.

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Practice: Subtracting Numbers Up to Five Digits With Borrowing

$91,447 - 23,016= $

a
 $66,234$
b
 $67,341$
c
 $67,234$
d
 $68,431$
e
 $66,134$
Practice: Subtracting Numbers Up to Five Digits With Borrowing

$13,247 - 9,515 =$

a
 $3,542$
b
 $2,632$
c
 $3,732$
d
 $4,632$
e
 $3,532$
Example: Subtracting Numbers Up to Five Digits: Word Problems

There are 32,355 bees in a hive. On a particular day, 12, 247 of the bees leave to find pollen. How many bees are left in the hive?

EXPLANATION

To determine how many bees are left in the hive, we need to calculate the value of

32, 355 - 12, 247.

First, we line up our numbers:

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 3 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 3 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 5 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 7 \!\!\! \\ \hline & & \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\!& \!\!\! \!\!\! \end{array}

Next, we proceed by subtracting the numbers in each place value from right to left, borrowing where needed.

\require{cancel} \begin{array}{cccccccc} & & \!\!\! & \!\!\! & \!\!\! & \!\!\! \color{blue}\substack{ \\ 4 } & \!\!\!\! \color{blue}\substack{ \\ 15 } \\ & & \!\!\! 3 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 3 \!\!\!& \!\!\!\!\! \cancel{5} \!\!\!& \!\!\!\!\! \cancel{5} \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 7 \!\!\! \\ \hline & & \!\!\! 2 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 1 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 8 \!\!\! \end{array}

Therefore, there are 20,108 bees left in the hive.

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Practice: Subtracting Numbers Up to Five Digits: Word Problems

There are $23,542$ people watching a baseball game at the stadium. If $15,631$ of them are adults, how many children are present at the game?

a
 $7,911$ children
b
 $7,851$ children
c
 $7,871$ children
d
 $7,902$ children
e
 $7,651$ children
Practice: Subtracting Numbers Up to Five Digits: Word Problems

During a period of two months, a bakery produced $20,524$ cupcakes. If, in the second month, they made $4,707$ cupcakes, how many cupcakes did the bakery produce in the first month?

a
 $15,297$ cupcakes
b
 $16,512$ cupcakes
c
 $16,307$ cupcakes
d
 $15,817$ cupcakes
e
 $15,217$ cupcakes
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