Problem Description:
The image contains a set of arithmetic problems involving integers. The task is to solve each problem and explain the solution.
Arithmetic Problems:
1. \(-4 + (-8)\)
2. \(9 + (-4)\)
3. \(-5 + (-9)\)
4. \(0 - (-4)\)
5. \(-8 + 7\)
6. \(3 + (-5)\)
7. \(-3 + (-7)\)
8. \(9 + (-4)\)
9. \(-5 + (-2)\)
10. \(9 + (-5)\)
11. \(-7 + (-9)\)
12. \(3 + (-4)\)
Solution Explanation:
####
Step 1: Understanding Integer Operations
-
Addition of Integers:
- Adding two positive integers results in a positive integer.
- Adding two negative integers results in a negative integer (sum of their absolute values).
- Adding a positive and a negative integer involves subtracting the smaller absolute value from the larger one, and the sign of the result depends on which number has the larger absolute value.
-
Subtraction of Integers:
- Subtracting a negative integer is equivalent to adding its positive counterpart.
- Subtracting a positive integer is straightforward subtraction.
####
Step 2: Solving Each Problem
1.
\(-4 + (-8)\)
- Adding two negative integers: \(-4 + (-8) = -(4 + 8) = -12\)
-
Answer: \(-12\)
2.
\(9 + (-4)\)
- Adding a positive and a negative integer: \(9 + (-4) = 9 - 4 = 5\)
-
Answer: \(5\)
3.
\(-5 + (-9)\)
- Adding two negative integers: \(-5 + (-9) = -(5 + 9) = -14\)
-
Answer: \(-14\)
4.
\(0 - (-4)\)
- Subtracting a negative integer is equivalent to adding its positive counterpart: \(0 - (-4) = 0 + 4 = 4\)
-
Answer: \(4\)
5.
\(-8 + 7\)
- Adding a negative and a positive integer: \(-8 + 7 = -(8 - 7) = -1\)
-
Answer: \(-1\)
6.
\(3 + (-5)\)
- Adding a positive and a negative integer: \(3 + (-5) = 3 - 5 = -2\)
-
Answer: \(-2\)
7.
\(-3 + (-7)\)
- Adding two negative integers: \(-3 + (-7) = -(3 + 7) = -10\)
-
Answer: \(-10\)
8.
\(9 + (-4)\)
- Adding a positive and a negative integer: \(9 + (-4) = 9 - 4 = 5\)
-
Answer: \(5\)
9.
\(-5 + (-2)\)
- Adding two negative integers: \(-5 + (-2) = -(5 + 2) = -7\)
-
Answer: \(-7\)
10.
\(9 + (-5)\)
- Adding a positive and a negative integer: \(9 + (-5) = 9 - 5 = 4\)
-
Answer: \(4\)
11.
\(-7 + (-9)\)
- Adding two negative integers: \(-7 + (-9) = -(7 + 9) = -16\)
-
Answer: \(-16\)
12.
\(3 + (-4)\)
- Adding a positive and a negative integer: \(3 + (-4) = 3 - 4 = -1\)
-
Answer: \(-1\)
Final Answers:
1. \(-12\)
2. \(5\)
3. \(-14\)
4. \(4\)
5. \(-1\)
6. \(-2\)
7. \(-10\)
8. \(5\)
9. \(-7\)
10. \(4\)
11. \(-16\)
12. \(-1\)
Boxed Final Answer:
\[
\boxed{-12, 5, -14, 4, -1, -2, -10, 5, -7, 4, -16, -1}
\]
Parent Tip: Review the logic above to help your child master the concept of printable integer games.
