Introduction

Let's compute the following difference:

1,456,546 - 1,224,292

As always, the first step is to line up our numbers according to their place value (ones over ones, tens over tens, hundreds over hundreds, and so on):

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 1 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 6 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 6 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 2 \!\!\! \\ \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{ \\ 14 } & \!\!\! \\ & & \!\!\! 1 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 6 \!\!\!& \!\!\!\!\! \cancel{5} \!\!\!& \!\!\!\!\! \cancel{4} \!\!\!& \!\!\! 6 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 2 \!\!\! \\ \hline & & & \!\!\! 2 \!\!\!& \!\!\! 3 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 4 \!\!\! \end{array}

Therefore, 1,456,546 - 1,224,292 = 232,254.

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Example: Subtracting Numbers Up to Seven Digits Without Borrowing

Compute the value of 1,487,645 - 45,214.

EXPLANATION

First, we line up our numbers:

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

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

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

Therefore, 1,487,645 - 45,214 = 1,442,431.

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Practice: Subtracting Numbers Up to Seven Digits Without Borrowing

$652,974 - 120,771 =$

a
 $523,403$
b
 $432,213$
c
 $432,203$
d
 $533,213$
e
 $532,203$
Practice: Subtracting Numbers Up to Seven Digits Without Borrowing

$5,256,479 - 1,120,177 =$

a
 $4,631,502$
b
 $4,126,305$
c
 $4,134,052$
d
 $4,136,302$
e
 $4,134,202$
Example: Subtracting Numbers Up to Seven Digits With Borrowing

What is 2,354,702 - 1,446,254?

EXPLANATION

First, we line up our numbers:

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 2 \!\!\!& \!\!\! 3 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 7 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 2 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 6 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 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{ \\ 1 } & \!\!\! \color{blue}\substack{ \\ 13 } & \!\!\! \color{blue}\substack{ \\ 4 } & \!\!\! \color{blue}\substack{ \\ 14 } & \!\!\! \color{blue}\substack{ \\ 6 } & \!\!\! \color{blue}\substack{ \\ 9 } & \!\!\! \color{blue}\substack{ \\ 12 } \\ & & \!\!\!\! \cancel{2} \!\!\!& \!\!\!\! \cancel{3} \!\!\!& \!\!\!\! \cancel{5} \!\!\!& \!\!\!\! \cancel{4} \!\!\!& \!\!\!\! \cancel{7} \!\!\!& \!\!\!\! \cancel{0} \!\!\!& \!\!\! 2 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 6 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 4 \!\!\! \\ \hline & & & \!\!\! 9 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 8 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 8 \!\!\! \end{array} Therefore, 2,354,702 - 1,446,254 = 908,448.

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Practice: Subtracting Numbers Up to Seven Digits With Borrowing

$7,456,785 - 2,324, 659 =$

a
 $5,322,134$
b
 $5,312,116$
c
 $5,131,236$
d
 $5,122,314$
e
 $5,132,126$
Practice: Subtracting Numbers Up to Seven Digits With Borrowing

$1,923,456 - 260,751 =$

a
 $662,705$
b
 $1,662,705$
c
 $1,632,305$
d
 $1,562,605$
e
 $562,605$
Example: Subtracting Numbers Up to Seven Digits: Word Problems

Mike, a baseball player, earns \[math]1, 245,800 per year, while Randy, a football player, makes \[/math]1,227,900 per year. How much more does Mike earn per year compared to Randy?

EXPLANATION

To find out how much more Mike earns compared to Randy, we need to calculate the value of

1, 245,800 - 1,227,900.

First, we line up our numbers:

\require{cancel} \begin{array}{cccccccc} & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 4 \!\!\!& \!\!\! 5 \!\!\!& \!\!\! 8 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 0 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 7 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 0 \!\!\! \\ \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{ \\ 14 } & \!\!\!\! \color{blue}\substack{ \\ 18 } & \!\!\! & \!\!\! \\ & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\!\!\! \cancel{4} \!\!\!\!& \!\!\!\!\! \cancel{5} \!\!\!\!& \!\!\!\!\! \cancel{8} \!\!\!\!& \!\!\! 0 \!\!\!& \!\!\! 0 \!\!\! \\ \!\!\!\!-\!\!\!\! & & \!\!\! 1 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 2 \!\!\!& \!\!\! 7 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 0 \!\!\! \\ \hline & & & & \!\!\! 1 \!\!\!& \!\!\! 7 \!\!\!& \!\!\! 9 \!\!\!& \!\!\! 0 \!\!\!& \!\!\! 0 \!\!\! \end{array}

Therefore, Mike earns \[math]17,900 more per year.

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Practice: Subtracting Numbers Up to Seven Digits: Word Problems

Mr. Lee wants to buy a piece of land valued at $\$758,623.$ If the bank has granted him a loan of $\$572,331,$ how much more money does Mr. Lee have to put in to buy the land?

a
 $\$\,126,212$
b
 $\$\,276,112$
c
 $\$\,176,312$
d
 $\$\, 286,392$
e
 $\$\,186,292$
Practice: Subtracting Numbers Up to Seven Digits: Word Problems

The population of the city last year was $2,002,789$ people. This year so far, $51,411$ people moved from the city to the suburbs. What is the current population of the city?

a
 $1,851,436$ people
b
 $1,951,378$ people
c
 $1,051,378$ people
d
 $1,931,346$ people
e
 $1,851,378$ people
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