Subtracting Whole Numbers

No Borrowing
To subtract whole numbers we write them as in an addition problem and subtract
each digit moving from the right to the left.
Example:
789
 34
Note that 9  4 =
5, 8  3 = 5, and 7  0
= 7
755

Borrowing is Necessary
If when subtracting digits, the top number is smaller than the bottom,
borrowing becomes necessary. We borrow one from the digit to the left.
Example:
Find 41  9
Solution
3
4
11
 9
We have written 41 as 30 + 11. Notice the
three in the new tens digit.
32
Example:
Find 1042  578
Solution
0
9
14 First
we write 52 as 40 + 12. Then notice that 0 can not be borrowed from,
1 0
512
 5 7 8
so we go to the next digit and write 104 as 90
+ 14.
47 4

Checking Your Work
We can think of subtraction as the reverse of addition.
Example
To check that 41  9 = 32, we can
work out 32 + 9:
1
32
+ 9
Since 2 + 9 = 11, we have carried
the 1.
41
Exercise
Check your work on the second example: 1052
 578 = 474

Solving for x
We can use this idea that subtraction is the inverse of addition when we
answer questions that ask to solve for x:
Example
Solve for x if
15 =
x + 11
Solution
We write the reverse of the addition problem which is a subtraction
problem. We have
x =
15  11
15
 11 Since
2 + 9 = 11, we have carried the 1.
4

Applications
Example
Consider the following table
taken for the United Nations world population figures (http://www.un.org/esa/population/pubsarchive/pop199900/pop199900.pdf)

How much did the world's total population
increase between 1999 and 2000?

In the year 2000, how many more people were
there in less developed countries vs. more developed countries?

In the year 1999, how many more people were
there in more developed countries vs. the least developed countries?
Solution
We subtract the two world populations:
5
9 14
14
6, 0 5 5, 10
4 9, 0 0 0
 5, 9 7 8, 4 0 1, 0 0 0
Since the numbers are in thousands, we tag
on three 0's
7 6, 6 4 8, 0 0 0
Between 1999 and 2000, the world population
increased by 76,648,000 poeple.
We subtract the more developed number
from the less developed number
15 16
9
4, 8 6 7, 0
16
9, 0 0 0
 1, 1 8 7, 9 8 0, 0 0 0
Since the
numbers are in thousands, we tag on three 0's
3,
6 7 9, 0 8 9, 0 0 0
In 2000, there were 3,679,089,000 more
people in less developed countries than in more developed countries.
We subtract the least developed number
from the more developed number
3
14 5
6 4 4, 6 17
7, 0 0 0
 6 2 9, 5 8 6, 0 0 0
Since the numbers are in thousands, we tag
on three 0's
1 5, 0 9 1, 0 0 0
In 1999, there were 15,091,000 more people in
more developed countries than in the least developed countries.
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