Question

$\frac{16}{9}$ is equal to 2 times which fraction?
$\frac{8}{9}$
$\frac{14}{9}$
$\frac{18}{9}$
$\frac{34}{9}$

Explanation:

Step1: Define the unknown fraction

Let the unknown fraction be $\frac{x}{y}$. The problem states that $2\times\frac{x}{y}=\frac{16}{9}$. To find $\frac{x}{y}$, we need to divide $\frac{16}{9}$ by 2.

Step2: Divide the fraction by 2

Dividing a fraction by a whole number is equivalent to multiplying the fraction by the reciprocal of the whole number. The reciprocal of 2 is $\frac{1}{2}$. So, $\frac{16}{9}\div2=\frac{16}{9}\times\frac{1}{2}$.

Step3: Multiply the fractions

When multiplying fractions, we multiply the numerators together and the denominators together. So, $\frac{16\times1}{9\times2}=\frac{16}{18}$.

Step4: Simplify the fraction

Simplify $\frac{16}{18}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, $\frac{16\div2}{18\div2}=\frac{8}{9}$.

Answer:

A. $\frac{8}{9}$