Download How do I add and subtract integers

How do I add and subtract integers?
As you remember in a prior lesson, an integer set includes whole numbers which are counting numbers
starting with 1 (1, 2, 3, 4…). An integer set also includes the set of whole numbers that are negative
(called negative integers; -1, -2, -3, -4). Integers also include the number zero (which is neither a
negative or positive number). The entire integer set is infinite so I will not list all of the numbers but for
the most part the integer set will look like this: …-3, -2, -1, 0, 1, 2, 3, 4…. The ellipses mean that the
set continues counting in both directions.
How do I add and subtract 2 integers? For the following addition and subtraction equations, I will use
the integer number line to help me solve. See the following examples:
1.
2.
3.
4.
5.
6.
7.
8.
5–3=?
4+3=?
5–6=x
–4 +2 = x
–4 – 2 = x
5 – (-2) = x
–5 – (-2) = x
–5 + (-2) = x
Before we get started on these problems, maybe think of each integer as money in an account. Either
you are “depositing or adding” money into the account or you are “withdrawing or subtracting” money
from your account. Lets look at the first 2 examples.
1. 5-3 = ?
You have been subtracting integers for a while and you may not have known that you were doing it!
Because 5-3=2, that means that ?=2 in this case.
2. 4+3 = ?
So 4+3 =7 so that means that ?=7 in this case.
Lets look at number 3.
3. 5 – 6 = x
In this problem it is like starting with 5 bucks in your account and spending 6. You now owe the bank 1
dollar (that is what the –1 means). In other words you are one dollar in debt. Since 5 –6 = -1, then x=-1
in this case.
Lets look at the rest of the problems. From now on there will be 2 problems on each number line.
4. –4+2 = x
5. –4-2 = x
In number 4, your bank account is overdrawn so you start out owing the bank $4 (this is why we start at
–4 on the number line. You deposit 2 dollars to get out of debt to pay them back (this is the +2). After
the dust settles so to speak, you still owe the bank 2 dollars. –4+2 = -2 so x=-2 in this case.
In number 5 you already owe the bank 4 dollars (-4). You spend 2 dollars, but because you do not really
have money to spend in your account, you will now owe the bank more. When the dust settles, you now
owe the bank $6 (that is your answer of –6). –4-2 = x so x = -6 in this case
Lets look at the last two problems.
6. 5 – (-2) = x
7. –5 – (-2) = x
In problem number 6 we are starting out with five dollars in our account. The bank made an error
(mistake) so they are going to forgive a past debt that you already paid back. They decide to forgive you
a 2-dollar debt. In other words they are subtracting a 2-dollar debt … - (-2). The first minus sign shows
that they are subtracting and the (–2) is the debt of 2 dollars. Because of this, the bank adds $2 to your
account. 5 – (-2) = 7 so x=7 in this case.
In problem number 7, we are starting out with a debt of five dollars in our account (this is the –5). The
bank decides you have been a good customer so they forgive a debt of two dollars (this is the –(-2) in the
problem. When they remove the two dollars of debt, you now only owe three dollars (this is the –3 in
your answer)! -5 – (-2) = -3 so this means x=-3 in this case.
8. –5 + (-2) = x
In problem 8 it is like I am in debt to my account $5 (-5). I use a credit card and spend 2 dollars. In
other words I am adding a debt of 2 dollars to my account. Now I am in debt $7. In this case x = -7.
Are you beginning to see how to add and subtract integers?
I hope you are now ready for the notes and independent practice. Please let me know at the beginning of
independent practice if you still need help. Thank you, and good luck.
Practice problems
Answer the following problems. Show all work.
1. The temperature dropped 12 degrees F in 8 hours. If the final temperature was –7 degrees F, what
was the starting temperature?
2. At 3 p.m., the temperature was 9 degrees F. By 11 p.m., it had dropped 30 degrees F. What was the
temperature at 11 p.m.?
3. Tad owes John $23 and borrows $12 more. How much does tad owe John now?
4. New Orleans, Louisiana is 6 ft. below sea level. The highest point in Louisiana, Driskill Mountain,
is 541 ft. higher than New Orleans. How high is Driskill Mountain?
5. A submarine submerged at a depth of –40ft. and dives 57 feet more. What is the new depth of the
submarine?
6. An airplane at 20,000 ft. drops 2,500 in altitude. What is the new altitude?
7. The daytime temperature on Mercury can reach 430 degrees C. The nighttime temperature can drop
to –180 degrees C. How much can the temperature drop during one day?
8. An ice cream company reported a net profit of $24,000 in 2002 and a net loss of $11,000 in 2003.
How much did the company’s profits change from 2002 to 2003?
9. A small business reported a net loss of 86,000 in 2004 and a net profit of 32,000 in 2005. How
much did the company’s profits change from 2004 to 2005?
10. The daytime high temperature of the Moon can reach 130 degrees C. At night, the temperature can
drop to –110 degrees C. What is the difference between the high and low temperature?