Question

Choose the correct option.
Statement 1: When a number/fraction is multiplied by a mixed number, the product will always be greater than the original number/fraction.
Statement 2: When a number/fraction is multiplied by a mixed number, the product will always be less than the original number/fraction.

• A. Only Statement $2$ is correct.
• B. Both statements are incorrect.
• C. Both statements are correct.
• D. Only Statement $1$ is correct.

Answer 1

The correct option is D Only Statement $1$ is correct.

Consider a number, say $\frac{1}{8}$, Multiply this fraction by a mixed number, say $1\frac{1}{8}$.
$\frac{1}{8}\times 1\frac{1}{8}$
Convert $1\frac{1}{8}$ to the standard form of fraction.
$1\frac{1}{8}=\frac{1\times 8+1}{8}=\frac{9}{8}$
Here, $\frac{9}{8}>1$
When a fraction is multiplied by another fraction greater than one, the product is greater than the original fraction.
$\frac{1}{8}\times \frac{9}{8}>\frac{1}{8}$.
So, this implies when a number/fraction is multiplied by a mixed number the product will always be greater than the original number, not less than the original fraction.
So, only Statement $1$ is correct.
Hence, Option B is correct.