Question

Fill in the blank.
$\frac{7}{9}\times$ _____ $>\frac{7}{9}$

• A. $\frac{1}{9}$
• B. $\frac{1}{7}$
• C. $1$
• D. $\frac{11}{9}$

Answer 1

The correct option is D $\frac{11}{9}$

Here, the product is greater than the original fraction. So, the missing fraction in the product must be greater than $1$.
This means the fraction should have a numerator greater than the denominator.
Hence, option B is correct.
Or

Option A:
When a fraction is multiplied by another fraction equal to one, the product is equal to the original fraction.
So, $\frac{7}{9}\times 1$ is not greater than $\frac{7}{9}$.

Option B:
$\frac{7}{9}\times \frac{11}{9}=\frac{7\times 11}{9\times 9}=\frac{77}{81}$
$\frac{7}{9}=\frac{7\times 9}{9\times 9}=\frac{63}{81}$
So,
$\frac{77}{81}>\frac{63}{81}$ and thus, $\frac{7}{9}\times \frac{11}{9}=\frac{77}{81}>\frac{7}{9}$
Hence, option B is correct.

Option C:
$\frac{1}{9}<1$
When a fraction is multiplied by another fraction less than one, the product is less than the original fraction.
So, $\frac{7}{9}\times \frac{1}{9}$ is not greater than $\frac{7}{9}$.

Option D:
$\frac{1}{7}<1$
When a fraction is multiplied by another fraction less than one, the product is less than the original fraction.
So, $\frac{7}{9}\times \frac{1}{7}$ is not greater than $\frac{7}{9}$.
Hence, Option B is correct.