Let the values of three mathematical expressions be represented by A, B, and C, where: A =… — ACT

Let the values of three mathematical expressions be represented by $A$ , $B$ , and $C$ , where:

A = -3^2 - ( -2 - 4 )^2 \div 3 \times 2

B = |-5 - (-3)| - 2^4 \div (-2)^3 \times (4 - 7)

C = \frac{4 - 3 \times 2^2}{2} - ( -1 )^5 \times 3

Arrange the expressions $A$ , $B$ , and $C$ in order from least to greatest numerical value.

Expression A, Expression B, Expression C

Evaluating each expression using correct PEMDAS order of operations yields

A = -33

B = -4

, and

C = -1

. Comparing these values gives the order from least to greatest as Expression A, followed by Expression B, followed by Expression C.

Evaluate Expression A by applying order of operations.

A = -33

Simplify the grouping

(-2 - 4) = -6

. Then apply exponents:

-3^2 = -9

and

(-6)^2 = 36

. Perform division and multiplication from left to right:

36 \div 3 \times 2 = 12 \times 2 = 24

. Subtract to find

-9 - 24 = -33

Evaluate Expression B by applying order of operations.

B = -4

Simplify grouping terms:

|-5 - (-3)| = 2

and

(4 - 7) = -3

. Evaluate exponents:

2^4 = 16

and

(-2)^3 = -8

. Perform division and multiplication from left to right:

16 \div (-8) \times (-3) = -2 \times (-3) = 6

. Subtract:

2 - 6 = -4

Evaluate Expression C by applying order of operations.

C = -1

Simplify the numerator:

4 - 3 \times 2^2 = 4 - 12 = -8

, so the fraction is

-4

. Evaluate the exponent:

(-1)^5 = -1

. Multiply:

-1 \times 3 = -3

. Subtract:

-4 - (-3) = -1

Compare the resulting values to determine the correct order from least to greatest.

Expression A (

-33

) < Expression B (

-4

) < Expression C (

-1

)

Comparing negative integers,

-33

is the smallest value and

-1

is the largest value.

Order of Operations and Number Properties

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