# 1.5 Subtraction of whole numbers  (Page 3/4)

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## Sample set e

Perform this subtraction.

The number 503 contains a single zero

1. The number to the immediate left of 0 is 5. Decrease 5 by 1.

$5-1=4$

2. Draw a line through the zero and make it a 10.
3. Borrow from the 10 and proceed.

$\text{1 ten}+\text{10 ones}$

$\text{10 ones}+\text{3 ones}=\text{13 ones}$

## Practice set e

Perform each subtraction.

888

4,543

8,669

## Borrowing from a group of zeros

Consider the problem

In this case, we have a group of zeros.

Since we cannot borrow any tens or hundreds, we must borrow 1 thousand. One thousand = 10 hundreds.

We can now borrow 1 hundred from 10 hundreds. One hundred = 10 tens.

We can now borrow 1 ten from 10 tens. One ten = 10 ones.

From observations made in this procedure we can suggest the following method for borrowing from a group of zeros.

## Borrowing from a group of zeros

To borrow from a group of zeros,
1. Decrease the digit to the immediate left of the group of zeros by one.
2. Draw a line through each zero in the group and make it a 9, except the rightmost zero, make it 10.
3. Proceed to subtract as usual.

## Sample set f

Perform each subtraction.

The number 40,000 contains a group of zeros.

1. The number to the immediate left of the group is 4. Decrease 4 by 1.

$4-1=3$

2. Make each 0, except the rightmost one, 9. Make the rightmost 0 a 10.

3. Subtract as usual.

The number 8,000,006 contains a group of zeros.

1. The number to the immediate left of the group is 8. Decrease 8 by 1.

$8-1=7$

2. Make each zero, except the rightmost one, 9. Make the rightmost 0 a 10.

3. To perform the subtraction, we’ll need to borrow from the ten.

$\begin{array}{c}\text{1 ten = 10 ones}\hfill \\ \text{10 ones + 6 ones = 16 ones}\hfill \end{array}$

## Practice set f

Perform each subtraction.

16,134

4,839

15,789,940

## Calculators

In practice, calculators are used to find the difference between two whole numbers.

## Sample set g

Find the difference between 1006 and 284.

 Display Reads Type 1006 1006 Press $-$ 1006 Type 284 284 Press = 722

The difference between 1006 and 284 is 722.

(What happens if you type 284 first and then 1006? We'll study such numbers in [link] Chapter 10.)

## Practice set g

Use a calculator to find the difference between 7338 and 2809.

4,529

Use a calculator to find the difference between 31,060,001 and 8,591,774.

22,468,227

## Exercises

For the following problems, perform the subtractions. You may check each difference with a calculator.

7

6

3

$\begin{array}{c}\hfill 56\\ \hfill \underline{-12}\end{array}$

$\begin{array}{c}\hfill 74\\ \hfill \underline{-33}\end{array}$

41

$\begin{array}{c}\hfill 80\\ \hfill \underline{-61}\end{array}$

$\begin{array}{c}\hfill 350\\ \hfill \underline{-141}\end{array}$

209

$\begin{array}{c}\hfill 800\\ \hfill \underline{-650}\end{array}$

$\begin{array}{c}\hfill 35,002\\ \hfill \underline{-14,001}\end{array}$

21,001

$\begin{array}{c}\hfill 5,000,566\\ \hfill \underline{-2,441,326}\end{array}$

$\begin{array}{c}\hfill 400,605\\ \hfill \underline{-121,352}\end{array}$

279,253

77,472

$\begin{array}{c}\hfill 42\\ \hfill \underline{-18}\end{array}$

$\begin{array}{c}\hfill 51\\ \hfill \underline{-27}\end{array}$

24

188

$\begin{array}{c}\hfill 242\\ \hfill \underline{-158}\end{array}$

$\begin{array}{c}\hfill 3,422\\ \hfill \underline{-1,045}\end{array}$

2,377

$\begin{array}{c}\hfill 5,565\\ \hfill \underline{-3,985}\end{array}$

$\begin{array}{c}\hfill 42,041\\ \hfill \underline{-15,355}\end{array}$

26,686

63,143,259

8,034

$\begin{array}{c}\hfill 59\\ \hfill \underline{-26}\end{array}$

33

$\begin{array}{c}\hfill 92,526,441,820\\ \hfill \underline{-59,914,805,253}\end{array}$

32,611,636,567

$\begin{array}{c}\hfill 30,000\\ \hfill \underline{-26,062}\end{array}$

3,938

$\begin{array}{c}\hfill 600\\ \hfill \underline{-216}\end{array}$

8,273,955

For the following problems, perform each subtraction.

Subtract 63 from 92.

The word "from" means "beginning at." Thus, 63 from 92 means beginning at 92, or $\text{92}-\text{63}$ .

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