Question

Which fraction equivalent to one makes this statement true?

6/9 ÷ ?/? = 2/3


(1 point)
Responses

1/1

2/2

3/3


4/4

Answer 1

To find the fraction that makes the statement true, we want to solve the equation:

\[
\frac{6}{9} \div \frac{x}{y} = \frac{2}{3}
\]

First, we can rewrite the division as multiplication by the reciprocal:

\[
\frac{6}{9} \times \frac{y}{x} = \frac{2}{3}
\]

Now, simplify \(\frac{6}{9}\):

\[
\frac{6}{9} = \frac{2}{3}
\]

So, now the equation is:

\[
\frac{2}{3} \times \frac{y}{x} = \frac{2}{3}
\]

To isolate \(\frac{y}{x}\), we divide both sides by \(\frac{2}{3}\):

\[
\frac{y}{x} = 1
\]

This means \(y = x\). The equivalent fraction that satisfies \(y/x = 1\) can be any fraction where both numerator and denominator are equal, such as:

- \(1/1\)
- \(2/2\)
- \(3/3\)
- \(4/4\)

Therefore, any of the choices would satisfy the original equation because they're all equal to 1.

For the most concise answer, we can choose:

**1/1**

as a valid response, since it directly represents one.