Integers Add and Subtract

Understanding Subtraction of Integers

Working with Integers

Remember when working with integers it is best to think of a context involing either temperature, elevation or money and debt to help reason your way through the problem.

Adding a negative is the same as subtracting.

For example we can think of 8 + -10 as being 8 degrees above zero and then dropping 10 degrees. The result would be -2 degrees.

The equations to the left are the same!

Do the following without a calculator!

Multiple Choice

How can $$26+\left(-32\right)$$ be written differently?

• $$-26-32$$

• $$26-32$$

Multiple Choice

$$8+\left(-2\right)$$

• -6

• 6

• -10

• 10

Multiple Choice

$$25+\left(-6\right)$$

• -31

• -19

• 19

• 31

Multiple Choice

$$5+\left(-12\right)$$

• -17

• -7

• 7

• 17

Multiple Choice

$$17+\left(-8\right)$$

• -25

• -9

• 9

• 25

Multiple Choice

$$8+\left(-19\right)$$

• -27

• -11

• 11

• 27

​When adding two negative numbers your result will be more negative. For example (-2) + (-4) = -6 . That would be like being in debt two dollars and then borrowing another 4. You would have 6 dollars in debt total.

Multiple Choice

$$-1+\left(-6\right)$$

• -7

• -5

• 5

• 7

Multiple Choice

$$-4+\left(-13\right)$$

• 17

• 9

• -9

• -17

Multiple Choice

$$-18+\left(-7\right)$$

• -11

• 11

• -25

• 25

​Subtracting a negative is the same thing as adding the positive. We can think of it as taking away debt. Or you may think of it as doing the oppostive of subtracting.

5 - (-2) is the same as 5 + 2

Multiple Choice

What is another way to write 2 - (-16)

• -2 + 16

• 2 + 16

• 2 + (-16)

Multiple Choice

What is $$10-\left(-3\right)$$ ?

• -13

• -7

• 7

• 13

Multiple Choice

What is $$29-\left(-5\right)?$$

• 34

• -34

• 24

• -24

Multiple Choice

What is $$4-\left(-18\right)?$$

• -22

• -14

• 22

• 14

Multiple Choice

What is $$12-\left(-14\right)?$$

• -2

• 26

• -2

• -26

Reorder

Order the following from least to greatest.

$$-\frac{1}{2},\ -0.6,\ 0.6,\ \frac{1}{10},\ -7$$

• -7

• $$-0.6$$

• $$-\frac{1}{2}$$

• $$\frac{1}{10}$$

• 0.6

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

Which expression is equivalent to $$-3-\left(-8\right)?$$

• 3 + 8

• -3 + 8

• 3 - 8

• -3 + (-8)

Multiple Choice

What is $$-11-\left(-2\right)$$ ?

• -13

• -9

• 9

• 13

Multiple Choice

What is $$-24\ -\left(-7\right)$$ ?

• -31

• 31

• -17

• 17

Multiple Choice

What is $$3+\left(-14\right)$$ ?

• -17

• 17

• -11

• 11

Multiple Choice

What is $$\left(-27\right)+\left(-3\right)$$ ?

• -30

• -24

• 30

• 24

Multiple Choice

What is equivalent to $$8-\left(-15\right)$$ ?

• $$8+15$$

• $$-8+15$$

• $$8-15$$

• $$-8-15$$

Multiple Choice

What is eqivalent to $$-9+\left(-19\right)$$ ?

• $$-9+19$$

• $$-9-19$$

Multiple Choice

What is $$-9+\left(-19\right)$$

• 28

• -28

• 10

• -10

Multiple Choice

What is another way to write $$-13-\left(-20\right)$$ ?

• $$13+20$$

• $$-13+20$$

• $$13-20$$

• $$-13-20$$

Multiple Choice

What is $$-20+\left(-2\right)$$

• -18

• 18

• -22

• 22

Multiple Choice

On the first play of a game, the Eagles

running back lost three yards. On their next

play, the quarterback was sacked for a loss

of fourteen yards. Find the total yards in

these two plays.

• -11 yards

• -17 yards

• 11 yards

• 17 yards

Multiple Choice

Brett and Max are diving. Brett is 34 feet

below the surface and Max is 25 feet below

the surface. How many feet above Brett is

Max?

• 9 feet

• 59 feet

Multiple Choice

Once a hot-air balloon reached its highest

point, it dropped 25 feet. Then five minutes

later, it dropped another 13 feet. Find its

total change in altitude during this time.

• -25 feet

• -13 feet

• -12 feet

• -38 feet

Multiple Choice

At sunset, the temperature was 4 degrees.

Then at sunrise the next morning, it was -7

degrees. What is the difference between

these temperatures?

• 11 degrees

• 4 degrees

• 7 degrees

• 3 degrees

Multiple Choice

Nick’s bank accout balance was $21. If he

writes a check for $30 and his bank charges

him $35 for overdrawing his account, find

his account balance.

• 9

• -9

• -51

• -44

Reorder

List the following from least to greatest.

$$0.9,\ -\frac{8}{10},\ -\frac{1}{10},-0.9,\ -\frac{1}{2}$$

• $$-0.9$$

• $$-\frac{8}{10}$$

• $$-\frac{1}{2}$$

• $$-\frac{1}{10}$$

• $$0.9$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5