When you add or subtract two integers, the sum or the difference is also an integer. Algebra tiles can be used as a model for subtraction of integers. In the examples below, you can see how addition and subtraction of integers are related.
In the examples above, notice that –3 – (–1) = –3 + 1.
In the examples above, notice that –2 – 1= –2 + (–1). This
example shows that subtracting 1 from 2 is the same as adding 1 to 2.
The examples on the previous page suggest that subtracting an
integer is the same as adding the additive inverse or opposite of the integer.
Example
Find each difference.
1.
6
– 4
Alternative Solutions :
6 – 4
= 6 + (–4) To subtract 4,
add –4.
= 2 Simplify.
2.
–5
– (–3)
Alternative Solutions :
–5 – (–3)
= –5 + 3 To subtract –3, add 3.
= –2 Simplify.
3.
–3
– 2
Alternative Solutions :
–3 – 2
= –3 + (–2) To subtract 2, add –2.
= –5 Simplify.
4.
4
– (–1)
Alternative Solutions :
4 – (–1)
= 4 + 1 To subtract –1, add 1.
= 5 Simplify.
5.
2
– 5
Alternative Solutions :
2 – 5 =
2 + (–5) To subtract 5, add –5.
= –3 Simplify.
6.
–3
– (–6)
Alternative Solutions :
–3 – (–6)
= –3 + 6 To subtract –6, add 6.
= 3 Simplify
When you evaluate expressions, it is helpful to write any
subtraction expressions as addition expressions first.
Example
7.
Evaluate x – y if x = –2 and y = 1.
Alternative Solutions :
x – y = –2 – 1
Replace x with –2 and y with 1.
= –2 + (–1) Write –2 – 1 as –2 + (–1).
= –3 –2 + (–1) = –3
8.
Evaluate a – b + c if a = 6, b = –2, and c = –6.
Alternative Solutions :
a – b + c = 6 – (–2) + (–6) Replace
a with 6, b with –2, and c with –6.
= 6 + 2 + (–6) Write 6 – (–2) as 6 + 2.
= 8 + (–6) 6 + 2 = 8
= 2 8
+ (–6) = 2
Integers are often used to show how data has changed for a
given time.
Example
Population Link
9. The
map shows the number of people who moved to Ohio from Indiana in a recent year.
It also shows the number of people who left Ohio for Indiana. The change in
Ohio’s population p can be found by
using the formula p = m – l,
where m is the number of people moving
to Ohio and l is the number of people leaving Ohio.
Alternative Solutions :
Find
the net change in Ohio’s population resulting from people moving to and from
Indiana.
p = m – l
p = 9645 – 12,395 Replace m with 9645 and
l with 12,395
p = 9645 – 12395
= –2750
p = –2750 Ohio’s
population decreased by 2750 people.
Sumber
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