Evaluate each of the following numerical expressions using the standard order of operation… — ACT

Evaluate each of the following numerical expressions using the standard order of operations. Arrange the expressions in order of their simplified values from least to greatest.

1 $12 - 3 \times | -4 + 1 |$
2 $18 \div 3 \times 2 - 2^3$
3 $(6 - 8)^2 \div 2 + 3$
4 $-2^2 + 5 \times (3 - 1)$

Answer

The correct order of the expressions from least to greatest simplified value is:

12 - 3 \times | -4 + 1 |

(value of 3),

18 \div 3 \times 2 - 2^3

(value of 4),

(6 - 8)^2 \div 2 + 3

(value of 5), and

-2^2 + 5 \times (3 - 1)

(value of 6).

Evaluating each expression according to the correct order of operations results in values of 3, 4, 5, and 6, respectively.

Step-by-Step Solution

Evaluate the expression

12 - 3 \times | -4 + 1 |

3

Simplify inside the absolute value first:

-4 + 1 = -3

. Taking the absolute value gives

|-3| = 3

. Perform multiplication before subtraction:

3 \times 3 = 9

. Subtract:

12 - 9 = 3

Evaluate the expression

18 \div 3 \times 2 - 2^3

4

Evaluate the exponent first:

2^3 = 8

. Perform multiplication and division from left to right:

18 \div 3 = 6

and

6 \times 2 = 12

. Subtract:

12 - 8 = 4

Evaluate the expression

(6 - 8)^2 \div 2 + 3

5

Simplify inside parentheses:

6 - 8 = -2

. Apply the exponent:

(-2)^2 = 4

. Divide:

4 \div 2 = 2

. Add:

2 + 3 = 5

Evaluate the expression

-2^2 + 5 \times (3 - 1)

6

Apply the exponent to the base 2:

-2^2 = -4

. Evaluate inside parentheses:

3 - 1 = 2

. Multiply:

5 \times 2 = 10

. Add:

-4 + 10 = 6

Key Concept

Using the standard order of operations (PEMDAS/GEMS) to evaluate numerical expressions containing exponents, grouping symbols, absolute values, multiplication, division, addition, and subtraction.

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