Question

evaluate each expression.

1. $(-5)^2 - 3$
2. $-4 \div -1 - 3$
3. $3 - 4 \times -3$
4. $6 \times -2 - 5$
5. $(-3) - (-8) - (3 + 2)$
6. $3 - (-3) - 2 + 10$
7. $(-8) \times 6 - (-9) \times 9$
8. $\frac{7 \times 3}{3} + 8$

Explanation:

Problem 20: $(-5)^2 - 3$

Step 1: Calculate the square

First, we calculate $(-5)^2$. By the definition of squaring a number, $(-5)^2 = (-5) \times (-5) = 25$.

Step 2: Subtract 3

Then we subtract 3 from the result: $25 - 3 = 22$.

Step 1: Perform the division

First, we do the division: $-4 \div -1 = 4$ (since dividing two negative numbers gives a positive result).

Step 2: Subtract 3

Then we subtract 3: $4 - 3 = 1$.

Step 1: Perform the multiplication

First, we calculate the multiplication: $4 \times -3 = -12$, but since there's a negative sign in front, it becomes $- (4 \times -3) = - (-12) = 12$ (or we can think of $3 - (4 \times -3) = 3 + 12$ because subtracting a negative is adding the positive). Wait, actually, using the order of operations (PEMDAS/BODMAS), we do multiplication first: $4 \times -3 = -12$, then we have $3 - (-12)$.

Step 2: Subtract the negative (add the positive)

Subtracting a negative number is the same as adding its positive counterpart, so $3 - (-12) = 3 + 12 = 15$.

Answer:

22

Problem 21: $-4 \div -1 - 3$