Question

lesson 1 - 3 add integers
quick review
to add integers with the same sign, add the
absolute value of each integer. the sign of
the sum will be the same as the sign of the
addends. to add integers with different signs,
find the difference of the absolute value of
each integer. the sign of the sum will be the
same as the sign of the greater addend.
example
find the sum of ((-28)+(-19)).
(|-28|+|-19|=28 + 19 = 47)
the sum of ((-28)+(-19)=-47).
find the sum of ((-28)+19).
(|-28|-|19|=28 - 19 = 9)
the sum of ((-28)+19=-9), because
(|-28|>|19|).
lesson 1 - 4 subtract integers
quick review
to subtract integers, use the additive inverse
to write an equivalent addition expression.
then follow the rules for addition. when
the signs are the same, find the sum of the
absolute values. when the signs are different,
find the difference. use the sign of the
number with the greater absolute value.
example
find (-7-(8)).
(-7+(-8)=-15)
the signs are the same, so the sum has the same
sign as the addends.
find (-7-(-8)).
(-7 + 8 = 1)
the signs are different, so the sign of the
difference is the same sign as the integer (8) with
the greater absolute value, which is positive.
practice

1. jonahs cell phone came with 64 gb of memory.

he has used 15 gb. he then uses 5 gb of
memory to record photos and videos from a trip.
use the addition expression (64+(-15)+(-5)) to
find how much memory is left on his phone.

1. stella walks down a flight of stairs to the

basement. then she walks back up the stairs
and up another flight of stairs to the second
floor of her house. each flight of stairs
represents a change of 12 feet in height.
how far is stella above the ground?

1. find the sum.

a. (64+(-15)) b. (-121+(-34))
c. (-86 + 92) d. (109+(-162))
practice

1. the temperature is (1^{circ}f) at dusk. it is 8 degrees

colder at dawn. what is the temperature at
dawn?

1. kyle and nadim are on the same space on a

board game they are playing. kyle moves back
2 spaces in one turn and moves back 3 more
spaces in his second turn. nadim has remained
in the same place. what integer represents
kyles location relative to nadims location on
the game board?

1. find the difference.

a. (82-(-14)) b. (-18-(-55))
c. (-17-44) d. (70-(-101))

Explanation:

Step1: Calculate the sum of used memory

First, find the total used memory. He used \(15\) GB and then \(5\) GB more. The total used is \(15 + 5=20\) GB.

Step2: Calculate the remaining memory

The initial memory is \(64\) GB. Using the formula \(remaining = initial - used\), we can rewrite it as an addition of integers: \(64+(- 20)\).
Since \(|64|>| - 20|\), we calculate \(64 - 20 = 44\). The sign is positive because \(64\) (the number with the greater absolute value) is positive.

Step1: Analyze Stella's movement

Stella walks down \(30\) feet (we can represent this as \(-30\)) and then walks up \(24\) feet (represented as \(+24\)).

Step2: Calculate the final position

Using the addition formula for integers \(-30 + 24\). Since \(| - 30|>|24|\), we calculate \(30 - 24=6\). The sign is negative because \(-30\) (the number with the greater absolute value) is negative.

a. \(64+(-15)\)

Since \(|64|>| - 15|\), we calculate \(64 - 15 = 49\). The sign is positive because \(64\) (the number with the greater absolute value) is positive.

b. \(-121+(-34)\)

The signs are the same. Add the absolute values: \(| - 121|+| - 34|=121 + 34 = 155\). The sign is negative.

c. \(-86 + 92\)

Since \(|92|>| - 86|\), we calculate \(92-86 = 6\). The sign is positive because \(92\) (the number with the greater absolute value) is positive.

d. \(109+(-162)\)

Since \(| - 162|>|109|\), we calculate \(162 - 109 = 53\). The sign is negative because \(-162\) (the number with the greater absolute value) is negative.

Step1: Use the subtraction rule

The temperature at dusk is \(1^{\circ}F\). It is \(8\) degrees colder at dawn. Using the formula \(T = 1-8\), which is equivalent to \(1+(-8)\).
Since \(| - 8|>|1|\), we calculate \(8 - 1=7\). The sign is negative because \(-8\) (the number with the greater absolute value) is negative.

Answer:

\(44\) GB