Which of the following is equivalent to (((3x)/(y)))/(((2x)/(7))) ? Choose 1 answer: (A) (21)/(2y) (B) 42 y (c) (2y)/(21) (D) (6x^(2))/(7y)

Problem Understanding: Understand the problem. We need to simplify the complex fraction (((3x)/(y)))/(((2x)/(7))).Rewriting the Complex Fraction: Rewrite the complex fraction as a division problem. The expression (((3x)/(y)))/(((2x)/(7))) can be rewritten as (3x/y) ÷ (2x/7).Using the Rule for Dividing Fractions: Use the rule for dividing fractions. To divide by a fraction, multiply by its reciprocal. So, (3x/y) ÷ (2x/7) becomes (3x/y) * (7/2x).Simplifying the Expression: Simplify the expression. Now we multiply the numerators and the denominators: (3x * 7) / (y * 2x). This simplifies to (21x) / (2xy).Canceling out Common Factors: Cancel out the common factors. We can cancel the x in the numerator and the denominator: (21~~x~~) / (2y~~x~~). This leaves us with 21 / (2y).Checking the Answer Choices: Check the answer choices. We compare our simplified expression with the given options and find that it matches with option (A) (21)/(2y).

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Which of the following is equivalent to
(((3x)/(y)))/(((2x)/(7))) ?
Choose 1 answer:
(A)
(21)/(2y)
(B)
42 y
(c)
(2y)/(21)
(D)
(6x^(2))/(7y)

Which of the following is equivalent to $\frac{\left(\frac{3 x}{y}\right)}{\left(\frac{2 x}{7}\right)}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{21}{2 y}$ $\newline$ (B) $42 y$ $\newline$ (C) $\frac{2 y}{21}$ $\newline$ (D) $\frac{6 x^{2}}{7 y}$

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which of the following is equivalent to

\frac{\left(\frac{3 x}{y}\right)}{\left(\frac{2 x}{7}\right)}

\newline

Choose

1

answer:

\newline

(A)

\frac{21}{2 y}

\newline

(B)

42 y

\newline

(C)

\frac{2 y}{21}

\newline

(D)

\frac{6 x^{2}}{7 y}

Problem Understanding: Understand the problem. $\newline$ We need to simplify the complex fraction $\left(\frac{3x}{y}\right)/\left(\frac{2x}{7}\right)$ .
Rewriting the Complex Fraction: Rewrite the complex fraction as a division problem. $\newline$ The expression $\frac{3x}{y}$ / $\frac{2x}{7}$ can be rewritten as $\frac{3x}{y} \div \frac{2x}{7}$ .
Using the Rule for Dividing Fractions: Use the rule for dividing fractions. $\newline$ To divide by a fraction, multiply by its reciprocal. So, $(3x/y) \div (2x/7)$ becomes $(3x/y) \times (7/2x)$ .
Simplifying the Expression: Simplify the expression. $\newline$ Now we multiply the numerators and the denominators: $(3x \times 7) / (y \times 2x)$ . $\newline$ This simplifies to $(21x) / (2xy)$ .
Canceling out Common Factors: Cancel out the common factors. $\newline$ We can cancel the $x$ in the numerator and the denominator: $(21~~x~~) / (2y~~x~~)$ . $\newline$ This leaves us with $21 / (2y)$ .
Checking the Answer Choices: Check the answer choices. $\newline$ We compare our simplified expression with the given options and find that it matches with option (A) $\frac{21}{2y}$ .