If a = -2, b = 3, and c = -\frac{1}{2}, what is the value of the algebraic expression \fra… — ACT

If $a = -2$ , $b = 3$ , and $c = -\frac{1}{2}$ , what is the value of the algebraic expression $\frac{a^3 b + 4c}{a^2 - 2b}$ ?

Answer:If

a = -2

b = 3

, and

c = -\frac{1}{2}

, the value of the algebraic expression

\frac{a^3 b + 4c}{a^2 - 2b}

is 【13】.

Substituting

a = -2

b = 3

, and

c = -\frac{1}{2}

into the given expression yields a numerator of

(-2)^3(3) + 4(-\frac{1}{2}) = -24 - 2 = -26

and a denominator of

(-2)^2 - 2(3) = 4 - 6 = -2

. Dividing the numerator by the denominator gives

\frac{-26}{-2} = 13

Evaluate the terms in the numerator individually.

a^3 b = (-2)^3 \cdot 3 = -8 \cdot 3 = -24

and

4c = 4\left(-\frac{1}{2}\right) = -2

Exponents take precedence before multiplication, and multiplying a positive by a negative yields a negative number.

Combine the terms to calculate the numerator.

Numerator

= -24 + (-2) = -26

Adding two negative numbers sums their magnitudes with a negative sign.

Evaluate the terms in the denominator.

a^2 = (-2)^2 = 4

and

2b = 2(3) = 6

Squaring a negative base results in a positive value.

Calculate the denominator.

Denominator

= 4 - 6 = -2

Subtracting a larger number from a smaller number produces a negative result.

Divide the numerator by the denominator to find the final value.

\frac{-26}{-2} = 13

Dividing a negative number by a negative number yields a positive quotient.

Evaluating Algebraic Expressions

Estimated Time:1m 30s

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