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Perform this subtraction.
$\begin{array}{c}\hfill 503\\ \hfill \underline{-37}\end{array}$
The number 503 contains a single zero
The number to the immediate left of 0 is 5. Decrease 5 by 1.
$5-1=4$
Borrow from the 10 and proceed.
$\text{1 ten}+\text{10 ones}$
$\text{10 ones}+\text{3 ones}=\text{13 ones}$
Perform each subtraction.
$\begin{array}{c}\hfill 906\\ \hfill \underline{-18}\end{array}$
888
$\begin{array}{c}\hfill 5102\\ \hfill \underline{-559}\end{array}$
4,543
$\begin{array}{c}\hfill 9055\\ \hfill \underline{-386}\end{array}$
8,669
Consider the problem $\begin{array}{c}\hfill 5000\\ \hfill \underline{-37}\end{array}$
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.
Perform each subtraction.
$\begin{array}{c}\hfill \mathrm{40,000}\\ \hfill \underline{-125}\end{array}$
The number 40,000 contains a group of zeros.
The number to the immediate left of the group is 4. Decrease 4 by 1.
$4-1=3$
Make each 0, except the rightmost one, 9. Make the rightmost 0 a 10.
Subtract as usual.
$\begin{array}{c}\hfill \mathrm{8,000,006}\\ \hfill \underline{-\mathrm{41,107}}\end{array}$
The number 8,000,006 contains a group of zeros.
$8-1=7$
Make each zero, except the rightmost one, 9. Make the rightmost 0 a 10.
To perform the subtraction, we’ll need to borrow from the ten.
$\begin{array}{c}\text{1 ten = 10 ones}\hfill \\ \text{10 ones + 6 ones = 16 ones}\hfill \end{array}$
Perform each subtraction.
$\begin{array}{c}\hfill \mathrm{21,007}\\ \hfill \underline{-\mathrm{4,873}}\end{array}$
16,134
$\begin{array}{c}\hfill \mathrm{10,004}\\ \hfill \underline{-\mathrm{5,165}}\end{array}$
4,839
$\begin{array}{c}\hfill \mathrm{16,000,000}\\ \hfill \underline{-\mathrm{201,060}}\end{array}$
15,789,940
In practice, calculators are used to find the difference between two whole numbers.
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.)
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
For the following problems, perform the subtractions. You may check each difference with a calculator.
$\begin{array}{c}\hfill 15\\ \hfill \underline{-8}\end{array}$
7
$\begin{array}{c}\hfill 19\\ \hfill \underline{-8}\end{array}$
$\begin{array}{c}\hfill 11\\ \hfill \underline{-5}\end{array}$
6
$\begin{array}{c}\hfill 14\\ \hfill \underline{-6}\end{array}$
$\begin{array}{c}\hfill 12\\ \hfill \underline{-9}\end{array}$
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
$\begin{array}{c}\hfill 800\\ \hfill \underline{-650}\end{array}$
$\begin{array}{c}\hfill \mathrm{35,002}\\ \hfill \underline{-\mathrm{14,001}}\end{array}$
21,001
$\begin{array}{c}\hfill \mathrm{5,000,566}\\ \hfill \underline{-\mathrm{2,441,326}}\end{array}$
$\begin{array}{c}\hfill \mathrm{400,605}\\ \hfill \underline{-\mathrm{121,352}}\end{array}$
279,253
$\begin{array}{c}\hfill \mathrm{46,400}\\ \hfill \underline{-\mathrm{2,012}}\end{array}$
$\begin{array}{c}\hfill \mathrm{77,893}\\ \hfill \underline{-421}\end{array}$
77,472
$\begin{array}{c}\hfill 42\\ \hfill \underline{-18}\end{array}$
$\begin{array}{c}\hfill 51\\ \hfill \underline{-27}\end{array}$
24
$\begin{array}{c}\hfill 622\\ \hfill \underline{-88}\end{array}$
$\begin{array}{c}\hfill 261\\ \hfill \underline{-73}\end{array}$
188
$\begin{array}{c}\hfill 242\\ \hfill \underline{-158}\end{array}$
$\begin{array}{c}\hfill \mathrm{3,422}\\ \hfill \underline{-\mathrm{1,045}}\end{array}$
2,377
$\begin{array}{c}\hfill \mathrm{5,565}\\ \hfill \underline{-\mathrm{3,985}}\end{array}$
$\begin{array}{c}\hfill \mathrm{42,041}\\ \hfill \underline{-\mathrm{15,355}}\end{array}$
26,686
$\begin{array}{c}\hfill \mathrm{304,056}\\ \hfill \underline{-\mathrm{20,008}}\end{array}$
$\begin{array}{c}\hfill \mathrm{64,000,002}\\ \hfill \underline{-\mathrm{856,743}}\end{array}$
63,143,259
$\begin{array}{c}\hfill \mathrm{4,109}\\ \hfill \underline{-856}\end{array}$
$\begin{array}{c}\hfill \mathrm{10,113}\\ \hfill \underline{-\mathrm{2,079}}\end{array}$
8,034
$\begin{array}{c}\hfill 605\\ \hfill \underline{-77}\end{array}$
$\begin{array}{c}\hfill 59\\ \hfill \underline{-26}\end{array}$
33
$\begin{array}{c}\hfill \mathrm{36,107}\\ \hfill \underline{-\mathrm{8,314}}\end{array}$
$\begin{array}{c}\hfill \mathrm{92,526,441,820}\\ \hfill \underline{-\mathrm{59,914,805,253}}\end{array}$
32,611,636,567
$\begin{array}{c}\hfill \mathrm{1,605}\\ \hfill \underline{-881}\end{array}$
$\begin{array}{c}\hfill \mathrm{30,000}\\ \hfill \underline{-\mathrm{26,062}}\end{array}$
3,938
$\begin{array}{c}\hfill 600\\ \hfill \underline{-216}\end{array}$
$\begin{array}{c}\hfill \mathrm{9,000,003}\\ \hfill \underline{-\mathrm{726,048}}\end{array}$
8,273,955
For the following problems, perform each subtraction.
Subtract 63 from 92.
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