Adding Integers with Different Signs

Adding Integers with Different Signs

You will learn how to use a number line and absolute value to solve problems.

How to use a number line.

• If the problem is 11 + (-4), we always start at 0.

• When we start at 0, we then move the number of spaces for the first number. If it is negative, we move to the left, and move to the right if it is positive.

• After we get to the number, we then move the number of spaces backwards or forwards for the number.

• EX. For the 11 + (-4), we move to the right 11 times and then the - 4 tells us to move backwards 4 times and we land on 7.

Fill in the Blank

Where do we always start on a number line?

Multiple Choice

Using a number line, solve 8 + (-4)

• 11

• 4

• -4

• -11

Multiple Choice

If the first number in a problem is negative, which way do you move?

• You move to the right.

• You move to the left.

Different Signs with Absolute Value

• We have the problem 11 + (-4).

• In order to solve, we need to find the absolute value of both numbers and then subtract those numbers.

• The absolute value of 11 and -4 is 11 and 4.

• We then subtract 11 - 4 and we get 7.

• In order to know if the answer is positive or negative, we need to see which absolute value is bigger.

• If the biggest absolute value is positive, the answer is positive. If the biggest absolute value is negative, the answer is negative.

Example

• The problem is -10 + 4.

• The absolute value for both is 10 and 4.

• We subtract 10 - 4 which equals 6.

• We know that 10 is bigger than 4 and when we look at our equations 10 is negative.

• The answer will be - 6 because 10 is negative.

Multiple Choice

12 + - 15

• 3

• -15

• 27

• -3

Multiple Choice

For the problem - 20 + 36, is the answer positive or negative?

• Positive

• Negative

Fill in the Blank

A whale swam at a depth of 275 ft below the surface of the ocean. After 10 minutes, it rose 194 feet. What number represents the location of the whale to the surface?

Fill in the Blank

At 5:00 pm a thermometer shows an outside temperature of 2° F. Then, over the next three hours, the temperature drops 11° F. What integer represents the thermometer reading, in degrees, at 8:00 pm?

Last thing will be adding multiple integers

• The problem is -26 + 74 + (-14)

• The first thing we can do is add the two negative numbers together because we will add them together. 

• -26 + (-14) = - 40

• Now what we have is - 40 + 74.

• Now we find the absolute values for each value and then subtract them.

• Absolute value of - 40 and 74 is 40 and 74. When we subtract those, the answer is 74 - 40 = 34.

• The answer is going to be positive 34 because 74 is positive.

Multiple Choice

Find −14+8+(−6)

• -28

• -12

• 28

• 12

Multiple Choice

–21 + (–9) + 18

• -12

• 38

• -38

• -11

Multiple Choice

A roller coaster starts at point A, 43 ft above ground. It ascends 55 ft, descends 80 ft, and ascends 110 ft to point B. What is the height of the roller coaster at point B in relation to the ground?

• 110

• 80

• 128

• -90

Multiple Choice

In 30 seconds, a mountain biker goes up a 125-foot hill, then down 78 feet, and then back up a 32-foot hill. How much higher or lower from the start of the trail is the biker after 30 seconds?

• -15

• 79

• 68

• -32