Let's go through the problems step by step.

Fill in the Blanks:

1. The additive identity for integers is 0.
2. The multiplicative identity for integers is 1.
3. The product of any integer and 0 is 0.
4. The quotient of any non-zero integer divided by itself is 1.
5. The product of a negative integer and a positive integer is always negative.

True or False:

1. The sum of two negative integers is always positive. False (it’s always negative).
2. The difference of two positive integers can be negative. True (if the first integer is smaller than the second).
3. The product of three negative integers is negative. False (it is positive because an odd number of negatives multiplied gives a negative result).
4. The quotient of a negative integer divided by a positive integer is always negative. True.
5. The absolute value of a positive integer is always negative. False (the absolute value is always non-negative).

Solve the Following:

1. Find the sum of -12 and 8.
   -12 + 8 = -4

2. Subtract -5 from 13.
   13 - (-5) = 13 + 5 = 18

3. Multiply -4 by -7.
   -4 × -7 = 28

4. Divide 24 by -3.
   24 ÷ -3 = -8

5. Evaluate (-3) × (-2) + 5.
   (-3) × (-2) = 6
   6 + 5 = 11

Word Problems:

1. The temperature in the morning was -5°C. In the afternoon, it rose by 8°C. What was the temperature in the afternoon?
   -5°C + 8°C = 3°C

2. A submarine was at a depth of -150 meters. It rose 75 meters. What is its new depth?
   -150 + 75 = -75 meters

3. A football team lost 5 yards on the first play, gained 8 yards on the second play, and lost 3 yards on the third play. What was their total yardage?
   -5 + 8 - 3 = 0 yards

Do you have any questions about these problems? Would you like more detailed explanations on any specific part?

Related Questions:

1. What is the additive inverse of any integer?
2. What happens when you multiply two negative numbers?
3. How can you determine the sign of a quotient involving negative integers?
4. How do you find the absolute value of a number?
5. What is the result of subtracting a positive number from a negative number?

Tip:

When dealing with positive and negative integers, remember that adding a negative number is the same as subtracting, and subtracting a negative number is the same as adding.