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1.13 Additive inverses

Worksheet
Additive inverses
1

Describe - \left( - 1 \right) in words.

2

Simplify - \left( - 70 \right).

3

Fill in the blank to make the following statements true:

a
8 - 13 = 8 + ⬚
b
4 - 5 = 4 + ⬚
c
9 - \left( - 17 \right) = 9 + ⬚
d
- 2 - \left( - 5 \right) = - 2 + ⬚
4

For each of the following subtractions:

i

Rewrite it as an addition.

ii

Find the final value.

a
9 - \left( - 8 \right)
b
- 3 - \left( - 2 \right)
c
10 - \left( - 5 \right)
d
- 6 - \left( - 4 \right)
e
-11 - \left( - 20 \right)
f
- 7 - \left( - 12 \right)
g
24 - \left( - 16 \right)
h
- 16 - \left( - 24 \right)
5

State the additive inverse of the following:

a
- 23
b
27
c
- \dfrac{4}{9}
d
\dfrac{1}{5}
e
0.8
f
- 5.23
g
a
h
- s
6

Find the value of:2 - \left( - 5 \right) - \left( - 1 \right)

7

Consider the addition 1 + \left( - 8 \right).

a

Which one of the following calculations could we use to evaluate 1 + \left( - 8 \right)?

A
1 + \left( - 8 \right) = 1 + \left( - 1 \right) + 7
B
1 + \left( - 8 \right) = 1 - 1 + 7
C
1 + \left( - 8 \right) = 1 + 1 - 7
D
1 + \left( - 8 \right) = 1 + \left( - 1 \right) + \left( - 7 \right)
b

Evaluate 1 + \left( - 8 \right).

8

Consider the subtraction 4 - \left( - 3 \right).

a

State the additive inverse of \left( - 3 \right).

b

Now, rewrite 4 - \left( - 3 \right) as the sum of 4 and the additive inverse of \left( - 3 \right).

9

If v is an integer, then what does - \left( - v \right) equal?

10

The integers x and y are the same distance from 0 but on opposite sides. Find the value of x + y.

Applications
11

While surfing, a wave wipes Glen out and carries him 9 yards away from his board. A second wave carries him 8 yards further away. How many yards must he swim back to the board?

12

You have two numbered cards in your hand. The sum of the numbers is 0. If the number on one of the cards is 6, state the number on the other card.

13

If the temperature rises from - 2\degree \text{F} to 22\degree \text{F} in 11 minutes. By how much did the temperature rise?

14

Nanga Parbat is a mountain that is 8126 meters above sea level.

a

State the integer used to represent the elevation of the mountain.

b

State the additive inverse of this elevation.

c

Evaluate 8126 + \left( - 8126 \right) .

d

Describe what the additive inverse might represent in this context.

15

In the last financial year, Delicious Donuts had an overall loss of \$88\,000.

a

State the integer used to represent how much money the company made.

b

State the additive inverse of this result.

c

Evaluate - 88\,000 + 88\,000.

d

Describe what the additive inverse might represent in this context.

16

Luke is currently scuba diving at an elevation of - 24 meters.

a

State the integer used to represent the elevation.

b

State the additive inverse of this elevation.

c

Evaluate - 24 + 24.

d

Describe what the additive inverse might represent in this context.

17

The current temperature is 24\degree \text{C}. Over the next 8 hours the temperature decreases and then increases, returning back to 24\degree \text{C}. If the temperature initially decreased by 14\degree \text{C}, by how much did it subsequently increase?

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Outcomes

MA.6.NSO.4.1

Apply and extend previous understandings of operations with whole numbers to add and subtract integers with procedural fluency.

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