Question

Choose a fraction that can be multiplied by $\frac{7}{9}$ to get a product greater than $\frac{7}{9}.$

• A. $\frac{9}{9}$
• B. $\frac{1}{9}$
• C. $\frac{19}{9}$
• D. $\frac{7}{9}$

Answer 1

The correct option is C $\frac{19}{9}$

A fraction that can be multiplied by $\frac{7}{9}$ to get a product greater than $\frac{7}{9}$ means:
$\frac{7}{9}\times$ ___ $>\frac{7}{9}$.
So, we have to choose a fraction such that $\frac{7}{9}\times$ ___ $>\frac{7}{9}$
Here, the product is greater than the original fraction. So, the fraction in the product must be greater than $1$.
This means the fraction should have a numerator greater than the denominator.
So, option A is correct.
Or

Option A:
Here, $\frac{19}{9}>1$
When a fraction is multiplied by a fraction greater than $1$, it gives a product greater than the original fraction.
So, $\frac{7}{9}\times \frac{19}{9}>\frac{7}{9}$

Option B:
Here, $\frac{7}{9}<1.$
When a fraction is multiplied by another fraction less than one, the product is less than the original fraction.
So, $\frac{7}{9}\times \frac{7}{9}<\frac{7}{9}$

Option C:
Here,
$\frac{1}{9}<1.$
When a fraction is multiplied by another fraction less than one, the product is less than the original fraction.
So, $\frac{7}{9}\times \frac{1}{9}<1$

Option D:
Here, $\frac{9}{9}=1.$
When a fraction is multiplied by another fraction equal to one, the product is equal to the original fraction.
So, $\frac{7}{9}\times 1=\frac{7}{9}$
Hence, Option A is correct.