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/pop1999-00/pop1999-00.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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