Which of the following expressions is equivalent to (8p+8)/(-32 p+4) ? Choose 1 answer: (A) (p+2)/(-4p+1) (B) (2p+2)/(-8p+1) (C) (2p+2)/(8p+1) (D) (p+1)/(-8p+1)

Factor out common factor in numerator: Factor out the common factor in the numerator. The common factor in the numerator (8p + 8) is 8. So, we factor out 8 to get 8(p + 1).Factor out common factor in denominator: Factor out the common factor in the denominator. The common factor in the denominator (-32p + 4) is 4. So, we factor out 4 to get 4(-8p + 1).Simplify expression by dividing: Simplify the expression by dividing the numerator and the denominator by their common factor. We have 8(p + 1) / 4(-8p + 1). Divide both the numerator and the denominator by 4 to simplify the fraction. (8/4)(p + 1) / (4/4)(-8p + 1) = 2(p + 1) / (-8p + 1).Match simplified expression with choices: Match the simplified expression with the given choices. The simplified expression is 2(p + 1) / (-8p + 1). This matches with choice (D) (p + 1) / (-8p + 1).

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Which of the following expressions is equivalent to
(8p+8)/(-32 p+4) ?
Choose 1 answer:
(A)
(p+2)/(-4p+1)
(B)
(2p+2)/(-8p+1)
(C)
(2p+2)/(8p+1)
(D)
(p+1)/(-8p+1)

Which of the following expressions is equivalent to $\frac{8 p+8}{-32 p+4}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{p+2}{-4 p+1}$ $\newline$ (B) $\frac{2 p+2}{-8 p+1}$ $\newline$ (C) $\frac{2 p+2}{8 p+1}$ $\newline$ (D) $\frac{p+1}{-8 p+1}$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following expressions is equivalent to

\frac{8 p+8}{-32 p+4}

\newline

Choose

1

answer:

\newline

(A)

\frac{p+2}{-4 p+1}

\newline

(B)

\frac{2 p+2}{-8 p+1}

\newline

(C)

\frac{2 p+2}{8 p+1}

\newline

(D)

\frac{p+1}{-8 p+1}

Factor out common factor in numerator: Factor out the common factor in the numerator. $\newline$ The common factor in the numerator $(8p + 8)$ is $8$ . $\newline$ So, we factor out $8$ to get $8(p + 1)$ .
Factor out common factor in denominator: Factor out the common factor in the denominator. $\newline$ The common factor in the denominator $(-32p + 4)$ is $4$ . $\newline$ So, we factor out $4$ to get $4(-8p + 1)$ .
Simplify expression by dividing: Simplify the expression by dividing the numerator and the denominator by their common factor. $\newline$ We have $\frac{8(p + 1)}{4(-8p + 1)}$ . $\newline$ Divide both the numerator and the denominator by $4$ to simplify the fraction. $\newline$ $\frac{(\frac{8}{4})(p + 1)}{(\frac{4}{4})(-8p + 1)} = \frac{2(p + 1)}{-8p + 1}$ .
Match simplified expression with choices: Match the simplified expression with the given choices. $\newline$ The simplified expression is $\frac{2(p + 1)}{-8p + 1}$ . $\newline$ This matches with choice (D) $\frac{p + 1}{-8p + 1}$ .