# Integers - All Operations

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• 1.

### On the hottest day in Richmond, Virginia, the temperature was 105 degrees F.  On the coldest day, the temperature was 117 degrees F lower.  What was the coldest temperature in Richmond?

• A.

-117 degrees F

• B.

-12 degrees F

• C.

12 degrees F

• D.

117 degrees F

B. -12 degrees F
Explanation
105-117
105 + -117 LEAVE CHANGE CHANGE
Different signs - subtract the numbers and keep the sign of the one you have more of.

117-105 = 12

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• 2.

### Listed below are temperatures for four cities.  Using this information, determine which statement is true. Denver: -5 degrees F Chicago: -12 degrees F New York City: -8 degrees F Minneapolis: -15 degrees F

• A.

Chicago is colder than Denver, but warmer than New York City.

• B.

New York City is colder than Chicago and Minneapolis.

• C.

Denver is warmer than New York City and Minneapolis.

• D.

Denver is the coldest of the four cities listed.

C. Denver is warmer than New York City and Minneapolis.
Explanation
Further away from zero means that the city is colder. If you ordered the cities from wamest to coldest, it would be in this order:

Denver, New York City, Chicago, Minneapolis

Therefore, Denver is warmer than New York City and Minneapolis.

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• 3.

### Bryan swam to a depth of 29 feet below sea level while diving.  He descended another 31 feet.  He then rose up 16 feet.  Which process could be used to find Bryan's current depth?

• A.

• B.

• C.

• D.

Explanation
You start with -29 because below sea level is represented as a negative. To descend means to go down, so you would then subtract 31. If Bryan rose up, he went higher, so you would add 16.

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• 4.

### ABC Company lost \$21,000 in the first quarter of the year.  They lost the same amount each of the other three quarters.  Which integer represents the amount they lose for the year?  (Think about how many quarters there are in a whole year!)

• A.

\$63,000

• B.

-\$63,000

• C.

\$84,000

• D.

-\$84,000

D. -\$84,000
Explanation
There are FOUR quarters in a year.

If the company lost \$21,000, that would be represented as a negative integer. You would multiply
-\$21,000 by 4 to get the total amount lost for the year.

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• 5.

### Over a 4-month period, the total change in the average high temperature was -32 degrees.  What was the average change per month?

• A.

8 degrees

• B.

-128 degrees

• C.

-28 degrees

• D.

-8 degrees

D. -8 degrees
Explanation
If you know the total and the time period, you would divide to get the amount of change per month. If you have different signs when you are dividing integers, your answer will be negative.

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• 6.

### Which comparison is NOT true?

• A.

-15 > -13

• B.

-7 < 6

• C.

-23 < 22

• D.

8 > -8

A. -15 > -13
Explanation
Negative numbers are always smaller than positive numbers.

Numbers get smaller as they move further from zero.

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• 7.

### The entrance to a mine is 1,890 feet above sea level.  The bottom of a mine is 3,642 feet below the entrance.  What is the elevation at the bottom of the mine?

• A.

1,752 feet

• B.

5,532 feet

• C.

-1,752 feet

• D.

-5,532 feet

C. -1,752 feet
Explanation
Above sea level would be a positive integer. If the mine is below the entrance you would subtract.

1,890 - 3,642
1,890 + -3,642 (LEAVE CHANGE CHANGE)

Different signs - subtract the numbers and keep the sign of the one you have more of.

3,642 - 1,890 = 1,752

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• 8.

### Erin dives from the surface of a lake at a rate of 3 meters per minute.  At what depth, relative to the surface, is Erin after diving for 10 minutes?

• A.

-13 meters

• B.

-3.3 meters

• C.

-7 meters

• D.

-30 meters

D. -30 meters
Explanation
If Erin is diving underwater, it is represented by a negative integer. You know the amount she is going per minute (1 minute) and the total time that she dove, you would multiply the numbers to get the total depth.

-3 x 10

-3 x 10 = -30

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• 9.

### One day in Butte, Montana the temperature started out at 50 degrees.  Over the course of the day, the temperature dropped 4 degrees per hour for 6 consecutive hours.  Which procedure could be used to determine the temperature after 6 hours?

• A.

Divide 6 by – 4. Add the quotient to 50.

• B.

Divide 50 by 6. Add the quotient to – 4.

• C.

Multiply 4 by 6. Add the product to 50.

• D.

Multiply -4 by 6. Add the product to 50.

D. Multiply -4 by 6. Add the product to 50.
Explanation
If the temperature is dropping, that is represented by a negative number. You know how much it is dropping each hour and the total hours, so you would multiply the numbers to get the total amount the temperature dropped.

-4 x 6

This answer would then be added to the beginning temperature to get the current temperature.

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• 10.

### Billy has stock in Walmart.  The ending balance on the stock for the last five days were: +\$5, +\$2, -\$4, -\$8 and  -\$10.  What was the average daily change in Billy's stock?

• A.

-\$3

• B.

-\$15

• C.

\$29

• D.

-\$6

A. -\$3
Explanation
If you are finding an average, you would add all of the numbers and divide by how many numbers you have.

5 + 2 + -4 + -8 + -10 = -15

The stock dropped \$15 over a five day period, so you would divide to see how much it dropped per day.

-15 / 5 = -3

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