Question

problems 1-4: determine the value of each expression.

1. $5 + (-3)$
2. $-5 + 3$
3. $-5 - 3$
4. $-5 - (-3)$

Explanation:

Problem 1: \( 5 + (-3) \)

Step 1: Understand addition of signed numbers

Adding a negative number is like subtracting its absolute value. So \( 5 + (-3) = 5 - 3 \).

Step 2: Perform the subtraction

\( 5 - 3 = 2 \).

Step 1: Analyze the signs

We have two numbers with different signs. Subtract the smaller absolute value from the larger one. The absolute value of \( -5 \) is \( 5 \), and of \( 3 \) is \( 3 \). So \( | -5 | - | 3 | = 5 - 3 = 2 \).

Step 2: Determine the sign

Since the number with the larger absolute value (\( -5 \)) is negative, the result is negative. So \( -5 + 3 = - (5 - 3) = -2 \).

Step 1: Rewrite subtraction as addition

Subtracting a number is the same as adding its opposite. So \( -5 - 3 = -5 + (-3) \).

Step 2: Add the negative numbers

When adding two negative numbers, we add their absolute values and keep the negative sign. \( | -5 | + | -3 | = 5 + 3 = 8 \), so \( -5 + (-3) = -8 \).

Answer:

\( 2 \)

Problem 2: \( -5 + 3 \)