Question

evaluate each expression.

1. $24 \div 3 - 2 \cdot 3$
2. $5 + 2^2$
3. $4(3 + 9)$
4. $36 - 2(1 + 3)^2$
5. $\dfrac{40 - 2^3}{4 + 3(2^2)}$

Explanation:

Problem 6

Step1: Do division and multiplication first

$24\div3=8$, $2\cdot3=6$

Step2: Subtract the results

$8-6=2$

Problem 7

Step1: Calculate the exponent first

$2^2=4$

Step2: Add to the constant

$5+4=9$

Problem 8

Step1: Solve inside parentheses

$3+9=12$

Step2: Multiply by the outside factor

$4\times12=48$

Problem 9

Step1: Solve inside parentheses

$1+3=4$

Step2: Calculate the exponent

$4^2=16$

Step3: Multiply by the coefficient

$2\times16=32$

Step4: Subtract from the constant

$36-32=4$

Problem 10

Step1: Calculate exponents

$2^3=8$, $2^2=4$

Step2: Simplify numerator

$40-8=32$

Step3: Simplify denominator

$4+3\times4=4+12=16$

Step4: Divide numerator by denominator

$\frac{32}{16}=2$

Answer:

1. $2$
2. $9$
3. $48$
4. $4$
5. $2$