Adding & Subtracting Integers in Everyday Life

1. ADDING & SUBTRACTING
INTEGERS IN EVERY DAY LIFE

2. INTEGERS
 Integers are numbers that describe opposite ideas in
mathematics.
 Integers can either be negative(-), positive(+) or zero.
 The integer zero is neutral. It is neither positive nor
negative, but is an integer.
 Integers can be represented on a number line, which can
help us understand the valve of the integer.

3. ADDING INTEGERS
We can use a number line to help us add positive and negative integers.
–2 + 5 =
-2 3
= 3
To add a positive integer we move forwards up the number line.

4. We can use a number line to help us add positive and negative integers.
To add a negative integer we move backwards down the number line.
–3 + –4 == –7
-3-7
–3 + –4 is the same as –3 – 4
ADDING INTEGERS

5. 5-3
SUBTRACTING INTEGERS
We can use a number line to help us subtract positive and negative
integers.
5 – 8 == –3
To subtract a positive integer we move backwards down the number line.

6. 3 – –6 =
3 9
= 9
We can use a number line to help us subtract positive and negative
integers.
To subtract a negative integer we move forwards up the number line.
3 – –6 is the same as 3 + 6
SUBTRACTING INTEGERS

7. We can use a number line to help us subtract positive and negative
integers.
–4 – –7 =
-4 3
= 3
To subtract a negative integers we move forwards up the number line.
–4 – –7 is the same as –4 + 7
SUBTRACTING INTEGERS

8. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Integers LESS than ZERO
are negative integers
zero is neither
negative nor
positive
positives CAN
written with a (+)
sign (but not usually)
negatives are
written with a (-)
sign
Integers
Integers MORE than ZERO
are positive integers

9. VISUALIZING INTEGERS
0 1 2 3 4 5 6-1-2-3-4-5-6
+3 + -5 = -2
WHEN YOU ADD POSITIVE
NUMBERS…
GO TO THE RIGHT.
WHEN YOU ADD NEGATIVE
NUMBERS…
GO TO THE LEFT.

10. …an increase of 6 inches in height→ + 6
…earned 5 dollars interest → + 5
It is relatively easy to see the positive integers around us.
Negative integers however, may be a little less obvious.
…scored 10 fewer points → - 10
…a loss of 7 pounds → - 7
…temp of 9 degrees below zero → - 9
Integers - All Around Us!

11. INTEGERS IN MONEY
 Example: John owes $3, Virginia owes $5 but
Alex doesn't owe anything, in fact he has $3 in
his pocket. Place these people on the number line
to find who is poorest and who is richest.
 Having money in your pocket is positive.
 But owing money is negative.
 So John has "−3", Virginia "−5" and Alex "+3"
 Now it is easy to see that Virginia is poorer than
John (−5 is less than −3) and John is poorer than
Alex (−3 is smaller than 3), and Alex is, of course, the
richest!

12. INTEGERS IN MONEY
 Banks use integers to
represent the value of
transactions; these are
represented by means of
positive and negative
integers.
 The positive numbers
represent deposits while
the negative numbers
represent debits.
 Let’s look at the
integer rules and then
apply them to money
examples

13. ADDING INTEGERS: RULE 1
 If the signs (+ or -) are the same, simply add the
numbers and keep that value
 Example: 4 + 6 = 10
 Example:(+3) + (+4) = +7
 Example: -4 + -6 = -10
 Example:(-3) + (-4) = -7

14. MONEY: ADDING SAME SIGNS
 Example (positive plus a positive): Jude has $100 in
his savings account. On his birthday, Grandma
deposits $50 more into the account.
 +$100 + +$50 = $150
$100 00
Starting balance
Money from Grandma $150 00$50 00

15. MONEY: ADDING SAME SIGNS
 Example (negative plus a negative): Jack has
overdrawn his bank account by $100, so his
balance is now -$100. The check (debit) he wrote
to Kroger in the amount of $50 is presented. So
the bank subtracts $50 (-$50) more. (this added more
debt)
 -$100 + -$50 = -$150
Starting balance -$100 00
Kroger Grocery Store $50 00 -$150 00

16. ADDING INTEGERS: RULE 2
 If the signs are different, keep the sign of the
number furthest from zero. Either the most
positive or the most negative number.
 Example: 3 + -7 = -4
 Example: 12 + - 4 = 8
 Example: 10 + - 6 = 4
 Example: (-15) + (+11) = - 4

17. MONEY: ADDING DIFFERENT SIGNS
 Example (positive plus a negative): Jude has
$100 in his savings account. On Grandma’s
birthday, he withdraws $50 to buy her a
present. (this added a debit; but there is still more of a
credit; “positive” money)
 +$100 + -$50 = $50
Starting balance $100 00
$50 00Grandma’s gift $50 00

18. MONEY: ADDING DIFFERENT SIGNS
 Example (negative plus a positive): Jack has
overdrawn his bank account by $100 so his balance is
now -$100. He deposits $25 cash earned from mowing
lawns (credit). So the bank adds $25 to his debt. Now
his balance is -$75 (this added a credit; but there is still
more of a deficient; there’s more “negative” money)
 -$100 + $25 = -$75
Starting balance -$100 00
Lawn mowing money $25 00 -$75 00

19. SUBTRACTING INTEGERS: RULE 1
 If the signs are same. Subtraction is actually
adding it’s opposite. Change to addition by
changing the second number’s sign. Then follow
the addition rules.
 Example: +8 - +5 means = +8 + -5 = +3
Why? You’re adding a deficient to a positive amount
 Example: - 4 – -6 means - 4 + +6 = +2
Why? You’re subtracting a deficient from a negative amount;
that’s a positive move. Like adding the removal of a negative
amount.

20. MONEY: SUBTRACTING SAME SIGNS
 Example (positive minus a negative): Jude has
$100 in his savings account. On Grandma’s
birthday, he withdraws $50 to buy her a present
(+$100 - +$50). (subtracting money by adding a debit)
 +$100 + -$50 = $50
Starting balance $100 00
$50 00Grandma’s gift $50 00

21. MONEY: SUBTRACTING SAME SIGNS
 Example (negative minus a positive): Jack’s bank
account is overdrawn by $100 so his balance is -
$100. He deposits his lawn mowing money (credit) of
$25. So the bank subtracts $25 of his debt (-$100 - -$25).
This added credit to his debt.
 -$100 + $25 = -$75
Starting balance -$100 00
Lawn mowing money $25 00 -$75 00

22. SUBTRACTING INTEGERS: RULE 2
Subtraction simply changes itself to addition by
changing the second number’s sign. (add it’s
opposite.) Then follow the addition rules. Why?
You’re adding more deficient
 If the signs are different, you subtract and use
the sign of the number with the largest absolute
value. Again, either the most positive or the most
negative number.
 Example: +8 - -5 means = +8 + 5 = +13
 Example: -4 – +6 means -4 + -6 = -10

23. MONEY: SUBTRACTING DIFFERENT SIGNS
 Example (negative minus a positive): Jack’s bank
account is still overdrawn by $100 so his balance
is still -$100. He deposits his lawn mowing money
(credit) of $25. So the bank subtracts $25 of his debt.
 -$100 - +$25. This added credit to his debt.
 -$100 + $25 = -$75
Starting balance -$100 00
Lawn mowing money $25 00 -$75 00

24. MONEY: SUBTRACTING DIFFERENT SIGNS
How is subtracting a negative number be a positive move?
 Example (positive minus a negative): Jude has $100 in his
savings account. The bank accidently charged him a $30
service fee, leaving him a balance of $70 (+$100 + -$30 = +$70)
 The bank discovered the error and removed the charge. They
added the removal of a debit.
+$70 - -$30 = +$70 + +$30= +$100
Starting balance $100 00
Service charge $30 00
Service charge refund $100 00
$70 00
$30 00

25. BUDGETING APPLICATION
 Example: Kara earns $660/month after taxes.
 Based on her expenses below, is she living within her
means?
rent:$150
car payment:$125
car insurance: $75
food:$70
cell phone:$50
entertainment (movies, etc.):$100
misc.(gas, etc.):$55
 Her expenses are negative integers; her income is a
positive integer.
 -$150+ -$125+ -$75+ -$70+ -$50+ -$100+ -$55= -$625
 -$625+ $660 = $35

26. INTEGERS IN SPORTS
 Example: SCORES. You get positive marks when you score.
 You get negative marks when you are scored against.
 At the end of the game, your score gets balanced out based on
the positive and negative points you have scored.
 Example: Your home team scores 113 points and the guest team scores 108
points.
 113 + -108 = 5; your team was positive 5 points, so you win!

27. GOLF APPLICATION
• Your goal is to get the ball in the hole
"under par" or "on par," but not "over
par“ of the predetermined number of
strokes for that hole.
• Scores "under par," are reported as a
negative number and that is good! For
example, if par were 8 and you took 3
strokes to get the ball in the hole, your
score for that round would be a terrific
+3.
• Scores "over par," are reported as a
positive number of and that isn't so
good. For example, if par were 5 and
you took 8 strokes to get the ball in
the hole, your score for that round
would be an unfortunate +3.

28. PEITGEN
VOSS
Team Peitgen throws a pass from their 5 yard line and the pass
is completed for 40 yards. +5 yards + +40 yards = +45 yards
gained
If their quarterback is sacked and loses 20 yards, how many
total yards did they gain on the two plays combined? +45
yards – -20 yards = +25 yards
FOOTBALL APPLICATION
 Example: The number of yards towards your goal represents a positive integer
and the number of yards away from your goal represents a negative integer.

29. ELEVATOR APPLICATION
 Going up is a positive move and going down is
a negative move.
 Example: Ana enters the elevator from the
basement of the parking garage and takes it to
the 11th floor for lecture. 0+11=11
 Then she takes the elevator two floors down for a
workshop. What floor is she on? 11+(-2)=9
 On what floor will Ana be if she then goes down
seven floors for a snack. 9+(-7)=2
 How many flights did she travel in total (up and
down)? 11+2+7=20
up 11; down 2; down 7
12
11
10
9
8
7
6
5
4
3
2
1
B

30. CELL PHONE MINUTES APPLICATION
 Adie has a cell phone plan that
allows her to talk 25 anytime
minutes. +25
 She uses her cell phone to speak
to Tom for 15 minutes. -15
 She uses it again to talk 20
minutes to Grammy. -20
 How many minutes did Adie talk
on her cell phone? 35 minutes
 -15+ -20 (from plan) = (-35)
 How many minutes are left on
her plan (without rollover) or
how many minutes did she go
over her allowed minutes?
 +25+ -35 = (-10)
35
30
25
20
15
10
5
0
(Minutes)
10 minutes over

31. INTEGERS ON TIMELINES
 BC years are like negative numbers and AD years are like
positive numbers.
 Example: Nero was the Roman emperor from 54 to 68 AD. How long did
Nero rule? (hint: I’m moving to 68 AD from 54 AD; I’m subtracting 54
from 68) 68 -54=14years
 Example: The Punic Wars began in 264 B.C. and ended in 146 B.C. How
long did the Punic Wars last? (hint: 264 from 146) – 146 - - 264 = - 146 +
264 = 118 years
 Example: Roman Civilization began in 520 B.C. and ended in 454 A.D.
How long did Roman Civilization last? (hint: -520 from 454)
+454- -520 so +454 + 520 = 974 years

32. INTEGERS ON THERMOMETERS
Thermometers are really number lines that stand
upright. The numbers can be thought of as
temperature changes. Positive numbers (hotter) make
the temperature indicator rise. Negative numbers
(colder) make the temperature indicator fall.

33. WEATHER PROBLEM #1
 Example: In Buffalo, New York, the
temperature was -14°F in the
morning. If the temperature dropped
6°F, what is the temperature now?
 -14 + -6 = -20 degrees
 NOT 8 degrees

34. WEATHER PROBLEM #2
 Example: In the Sahara Desert one
day it was 110°F. In the Gobi Desert
a temperature of -50°F was recorded.
What is the difference between these
two temperatures?
 110 - -50 = 110 + 50 = 160 degrees
 NOT 60 degrees

35. TEMPERATURE PROBLEM
 Example: The melting point of
carbon disulfid is 115°F. The
freezing point of nitrogen is -114°F.
How much warmer is the melting
point of carbon disulfid than the
freezing point of nitrogen?
 115 - -114 = 115 + 114 = 229 degrees
 NOT 1 degree

36. INTEGERS IN SEA LEVEL/ELEVATION

37. 0 feet
250 feet
-275 feet
525
feet
250 - -275=
250 + 275=
 To move from a point above sea level to a point below sea level
(or visa versa), requires moving to sea level (0) first.
 Example: A helicopter is 250 feet above the surface of the ocean. The
submarine is positioned at 275 feet below sea level. What is the distance
from the helicopter to the submarine?

38. SEA LEVEL APPLICATION
 What is the distance between the plane flying at
5,000 ft. above to the submarine at -1,200 ft. below
sea level.
 So to figure the distance from this plane to the
submarine:
1. First, figure the distance from it’s altitude (5,000 ft.)
to sea level (0 ft.); 5,000 ft.
2. Next, figure the distance from sea level (0 ft.) to the
depth of the submarine (-1200 ft.); 1200 ft.
3. Then, add both distances; 5,000 +1,200= 6,200
 Example: Mt. Everest, the highest elevation in
Asia, is 29,028 feet above sea level. The Dead Sea,
the lowest elevation, is 1,312 feet below sea level.
What is the difference between these two
elevations? +29,028 - -1,312; 29,028 ft. + 1,312; so
29,028 ft. (down to 0) + 1,312 (from 0 down)= 30,340
 Example: A submarine was situated 800 feet below
sea level. If it ascends 250 feet, what is its new
position? (hint: adding to it’s depth). -800 + -250= -1050