Integers: Positive and Negative Numbers

1. -4 + (-7) + (-9) = _____

-18

-20

-12

-6

The given expression involves adding three negative numbers: -4, -7, and -9. When adding negative numbers, we can simply add their absolute values and then assign the negative sign to the sum. Thus, |-4| + |-7| + |-9| = 4 + 7 + 9 = 20. Since all three numbers are negative, the sum will also be negative. Therefore, the correct answer is -20.

Explanation

The given expression involves adding three negative numbers: -4, -7, and -9. When adding negative numbers, we can simply add their absolute values and then assign the negative sign to the sum. Thus, |-4| + |-7| + |-9| = 4 + 7 + 9 = 20. Since all three numbers are negative, the sum will also be negative. Therefore, the correct answer is -20.

2.

Complete the integer grid, and answer the following question. The top row across adds up to 17. What is the value of the PINK square?

+8

-8

+9

+10

The top row across adds up to 17, which means that the sum of the first three squares is 17. Since the first two squares are +8 and -8, the value of the third square must be +9 in order to make the sum equal to 17. Therefore, the value of the PINK square is +9.

Explanation

The top row across adds up to 17, which means that the sum of the first three squares is 17. Since the first two squares are +8 and -8, the value of the third square must be +9 in order to make the sum equal to 17. Therefore, the value of the PINK square is +9.

3.

Complete the integer grid, and answer the following question. The first column down adds up to 23. What is the value of the BLUE square?

8

9

10

11

The first column down adds up to 23. The sum of the numbers in the column is 8 + 9 + 10 + 11 = 38. Since the sum of the numbers in the column is 23, the value of the missing BLUE square can be calculated by subtracting the sum of the known numbers from the desired sum. Therefore, the value of the BLUE square is 23 - 38 = -15. However, since the grid is an integer grid, the value of the BLUE square cannot be negative. Therefore, it is not possible to determine the value of the BLUE square based on the given information.

Explanation

The first column down adds up to 23. The sum of the numbers in the column is 8 + 9 + 10 + 11 = 38. Since the sum of the numbers in the column is 23, the value of the missing BLUE square can be calculated by subtracting the sum of the known numbers from the desired sum. Therefore, the value of the BLUE square is 23 - 38 = -15. However, since the grid is an integer grid, the value of the BLUE square cannot be negative. Therefore, it is not possible to determine the value of the BLUE square based on the given information.

4. On Monday, in Alaska, the high temperature is -11 degrees. Tuesday's high temperature is predicted to be 9 degrees colder than Monday. But by Wednesday, the high temperature is going to improve, and be 20 degrees warmer than Tuesday. What is the high temperature going to be on Wednesday?

-10

11

0

-29

The question states that Tuesday's high temperature is predicted to be 9 degrees colder than Monday, which means it would be -20 degrees. Then, it states that Wednesday's high temperature is going to be 20 degrees warmer than Tuesday, which means it would be -20 + 20 = 0 degrees.

Explanation

The question states that Tuesday's high temperature is predicted to be 9 degrees colder than Monday, which means it would be -20 degrees. Then, it states that Wednesday's high temperature is going to be 20 degrees warmer than Tuesday, which means it would be -20 + 20 = 0 degrees.

5.

While teaching integers to the class, Mrs. Johnson uses her diet as an example. In January, Mrs. Johnson lost 8 pounds, and in February, she lost 5 more pounds. Frustrated with herself in March, she gained 10 pounds! Has Mrs. Johnson still lost weight, or has she gained even more?!

Can't tell, because I don't know what she weighed to start with...

Yes - she has still lost 8 pounds.

No - she has gained 23 pounds.

Yes - she has still lost 3 pounds.

Since we don't know Mrs. Johnson's initial weight, we cannot determine the exact amount of weight she has lost or gained. However, based on the given information, we can calculate the net change in her weight. Mrs. Johnson lost 8 pounds in January and then lost 5 more pounds in February. So, she has lost a total of 8 + 5 = 13 pounds. In March, she gained 10 pounds. Therefore, the net change in her weight is 13 - 10 = 3 pounds. Hence, she has still lost 3 pounds overall.

Explanation

Since we don't know Mrs. Johnson's initial weight, we cannot determine the exact amount of weight she has lost or gained. However, based on the given information, we can calculate the net change in her weight. Mrs. Johnson lost 8 pounds in January and then lost 5 more pounds in February. So, she has lost a total of 8 + 5 = 13 pounds. In March, she gained 10 pounds. Therefore, the net change in her weight is 13 - 10 = 3 pounds. Hence, she has still lost 3 pounds overall.

6. In Buffalo, New York, the temperature was ^-14°F in the morning. If the temperature dropped 7°F, what is the temperature now?

-7

0

-21

-28

The question states that the temperature in Buffalo, New York was -14°F in the morning. It then says that the temperature dropped 7°F. To find the new temperature, we need to subtract 7 from -14. When we subtract a negative number, it is the same as adding the positive equivalent. So, -14 - 7 is the same as -14 + (-7), which equals -21. Therefore, the new temperature is -21°F.

Explanation

The question states that the temperature in Buffalo, New York was -14°F in the morning. It then says that the temperature dropped 7°F. To find the new temperature, we need to subtract 7 from -14. When we subtract a negative number, it is the same as adding the positive equivalent. So, -14 - 7 is the same as -14 + (-7), which equals -21. Therefore, the new temperature is -21°F.

7. A submarine was situated 450 feet below sea level. If it descends 300 feet for 1 hour, and then rises 150 feet for the next 3 hours. At this point in time, how far is the submarine from exact sea level?

400 feet below sea level

Exactly at sea level

600 feet below sea level

200 feel below sea level

The submarine starts at 450 feet below sea level. It then descends an additional 300 feet, bringing it to 750 feet below sea level. After that, it rises 150 feet, which brings it back up to 600 feet below sea level. Therefore, the submarine is currently 600 feet below sea level.

Explanation

The submarine starts at 450 feet below sea level. It then descends an additional 300 feet, bringing it to 750 feet below sea level. After that, it rises 150 feet, which brings it back up to 600 feet below sea level. Therefore, the submarine is currently 600 feet below sea level.

8.

Complete the integer grid, and answer the following question. The middle column down adds up to 5. What is the value of the YELLOW square?

-2

4

6

-3

The middle column down adds up to 5, which means that the sum of the numbers in the middle column is equal to 5. The only number in the middle column that is missing is the value of the yellow square. Therefore, the value of the yellow square must be 5 minus the sum of the other numbers in the middle column. Since the sum of the other numbers in the middle column is -2 + 4 + (-3) = -1, the value of the yellow square is 5 - (-1) = 6.

Explanation

The middle column down adds up to 5, which means that the sum of the numbers in the middle column is equal to 5. The only number in the middle column that is missing is the value of the yellow square. Therefore, the value of the yellow square must be 5 minus the sum of the other numbers in the middle column. Since the sum of the other numbers in the middle column is -2 + 4 + (-3) = -1, the value of the yellow square is 5 - (-1) = 6.

Integers: Positive And Negative Numbers