Question

Choose a fraction that can be multiplied by $\frac{6}{7}$ to get a product less than $\frac{6}{7}$.

• A. $\frac{7}{6}$
• B. $\frac{8}{7}$
• C. $1$
• D. $\frac{1}{7}$

Answer 1

The correct option is D $\frac{1}{7}$

A fraction that can be multiplied by $\frac{6}{7}$ to get a product less than $\frac{6}{7}$ means:
$\frac{6}{7}\times$ ___ $<\frac{6}{7}$.
So, we have to choose a fraction such that $\frac{6}{7}\times$ ___ $<\frac{6}{7}$
Here, the fraction in the product is less than the original fraction. So, the fraction in the product must be less than $1$.
This means the fraction should have a numerator less than the denominator.

So, Option B is correct.
Or

Option A:
Here,
$\frac{8}{7}>1$
When a fraction is multiplied by another fraction greater than one, it gives a product greater than the original fraction.
$\frac{6}{7}\times \frac{8}{7}>\frac{6}{7}$

Option B:
Here, $\frac{1}{7}<1.$
When a fraction is multiplied by another fraction less than one, the product is less than the original fraction.
So, $\frac{6}{7}\times \frac{1}{7}<\frac{6}{7}$

Option C:
Here, $\frac{7}{6}>1$.
When a fraction is multiplied by another fraction greater than one, the product is greater than the original fraction.
So, $\frac{6}{7}\times \frac{7}{6}>\frac{6}{7}$

Option D:
When a fraction is multiplied by another fraction equal to one, the product is equal to the original fraction.
So, $\frac{6}{7}\times 1=\frac{6}{7}$
Hence, Option B is correct.