Which of the following expressions is equivalent to (49 r+14)/(42 r+42) ? Choose 1 answer: A) (7r+1)/(6r+3) (B) (7r+2)/(r+1) (C) (49 r+2)/(42 r+6) (D) (7r+2)/(6r+6)

Factor out common factors: Factor out the common factors in the numerator and the denominator. The numerator 49r + 14 can be factored by taking out the common factor of 7, which gives us 7(7r + 2). The denominator 42r + 42 can be factored by taking out the common factor of 42, which gives us 42(r + 1). So, (49r + 14)/(42r + 42) becomes (7(7r + 2))/(42(r + 1)).Simplify by canceling common factors: Simplify the expression by canceling out the common factors. We can divide both the numerator and the denominator by 7. This gives us (7r + 2)/(6(r + 1)).Expand denominator to check: Expand the denominator to check if it matches any of the answer choices. The denominator 6(r + 1) expands to 6r + 6. So, the simplified expression is (7r + 2)/(6r + 6).

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Which of the following expressions is equivalent to
(49 r+14)/(42 r+42) ?
Choose 1 answer:
A)
(7r+1)/(6r+3)
(B)
(7r+2)/(r+1)
(C)
(49 r+2)/(42 r+6)
(D)
(7r+2)/(6r+6)

Which of the following expressions is equivalent to $\frac{49 r+14}{42 r+42}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{7 r+1}{6 r+3}$ $\newline$ (B) $\frac{7 r+2}{r+1}$ $\newline$ (C) $\frac{49 r+2}{42 r+6}$ $\newline$ (D) $\frac{7 r+2}{6 r+6}$

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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{49 r+14}{42 r+42}

\newline

Choose

1

answer:

\newline

(A)

\frac{7 r+1}{6 r+3}

\newline

(B)

\frac{7 r+2}{r+1}

\newline

(C)

\frac{49 r+2}{42 r+6}

\newline

(D)

\frac{7 r+2}{6 r+6}

Factor out common factors: Factor out the common factors in the numerator and the denominator. $\newline$ The numerator $49r + 14$ can be factored by taking out the common factor of $7$ , which gives us $7(7r + 2)$ . $\newline$ The denominator $42r + 42$ can be factored by taking out the common factor of $42$ , which gives us $42(r + 1)$ . $\newline$ So, $(49r + 14)/(42r + 42)$ becomes $(7(7r + 2))/(42(r + 1))$ .
Simplify by canceling common factors: Simplify the expression by canceling out the common factors. $\newline$ We can divide both the numerator and the denominator by $7$ . $\newline$ This gives us $(7r + 2)/(6(r + 1))$ .
Expand denominator to check: Expand the denominator to check if it matches any of the answer choices. $\newline$ The denominator $6(r + 1)$ expands to $6r + 6$ . $\newline$ So, the simplified expression is $(7r + 2)/(6r + 6)$ .