Which of the following is equivalent to (((a+6)/(c)))/(((2a+6)/(2c))) ? Choose 1 answer: (A) (c)/(2) (B) (a+6)/(a+3) (C) (a+6)/(2(a+3)) (D) 1

Write Expression & Identify Operation: Write down the given expression and identify the operation involved. The given expression is a division of two fractions: (((a+6)/(c)))/(((2a+6)/(2c))). We need to divide the first fraction by the second fraction.Apply Division Rule: Apply the rule for dividing fractions, which is to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of ((2a+6)/(2c)) is (2c)/(2a+6). So, the expression becomes: ((a+6)/c) * (2c)/(2a+6).Simplify by Multiplying: Simplify the expression by multiplying the numerators and denominators. Multiply (a+6) by (2c) and c by (2a+6). This gives us: ((a+6) * (2c)) / (c * (2a+6)).Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. We can see that 2c is a common factor in both the numerator and the denominator. So, we can cancel out 2c from both to simplify the expression. This gives us: (a+6)/(2a+6).Check Further Simplification: Check if the expression can be simplified further. The expression (a+6)/(2a+6) cannot be simplified further as there are no common factors left to cancel out.

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Which of the following is equivalent to
(((a+6)/(c)))/(((2a+6)/(2c))) ?
Choose 1 answer:
(A)
(c)/(2)
(B)
(a+6)/(a+3)
(C)
(a+6)/(2(a+3))
(D) 1

Which of the following is equivalent to $\newline$ $\left(\frac{a+6}{c}\right)\div\left(\frac{2a+6}{2c}\right)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{c}{2}$ $\newline$ (B) $\frac{a+6}{a+3}$ $\newline$ (C) $\frac{a+6}{2(a+3)}$ $\newline$ (D) $1$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Which of the following is equivalent to

\newline

\left(\frac{a+6}{c}\right)\div\left(\frac{2a+6}{2c}\right)

\newline

Choose

1

answer:

\newline

(A)

\frac{c}{2}

\newline

(B)

\frac{a+6}{a+3}

\newline

(C)

\frac{a+6}{2(a+3)}

\newline

(D)

1

Write Expression & Identify Operation: Write down the given expression and identify the operation involved. $\newline$ The given expression is a division of two fractions: $\left(\frac{a+6}{c}\right)/\left(\frac{2a+6}{2c}\right)$ . $\newline$ We need to divide the first fraction by the second fraction.
Apply Division Rule: Apply the rule for dividing fractions, which is to multiply the first fraction by the reciprocal of the second fraction. $\newline$ The reciprocal of $(\frac{2a+6}{2c})$ is $(\frac{2c}{2a+6})$ . $\newline$ So, the expression becomes: $(\frac{a+6}{c}) \times (\frac{2c}{2a+6})$ .
Simplify by Multiplying: Simplify the expression by multiplying the numerators and denominators. $\newline$ Multiply $(a+6)$ by $(2c)$ and $c$ by $(2a+6)$ . $\newline$ This gives us: $\frac{(a+6) \cdot (2c)}{c \cdot (2a+6)}$ .
Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. $\newline$ We can see that $2c$ is a common factor in both the numerator and the denominator. $\newline$ So, we can cancel out $2c$ from both to simplify the expression. $\newline$ This gives us: $(a+6)/(2a+6)$ .
Check Further Simplification: Check if the expression can be simplified further. The expression $(a+6)/(2a+6)$ cannot be simplified further as there are no common factors left to cancel out.