Question

If we multiply a proper fraction with another proper fraction, then the value of the product would be what in comparison to the individual values of the proper fractions?

• A. Greater than the values of individual proper fractions
• B. Less than the values of individual proper fractions
• C. Equal to the values of individual proper fractions
• D. Cannot be determined

Answer 1

The correct option is B Less than the values of individual proper fractions

Let's take two different proper fractions as $\frac{4}{5}$ and $\frac{9}{10}$.

The values of these proper fractions are
$\frac{4}{5}=0.8$ and $\frac{9}{10}=0.9$

Multiplying the proper fractions and finding the value of the product:
Product $=\frac{4}{5}\times \frac{9}{10}=0.8\times 0.9=0.72$

$\therefore 0.72<0.8\Rightarrow (\frac{4}{5}\times \frac{9}{10})<\frac{4}{5}$ and
$0.72<0.9\Rightarrow (\frac{4}{5}\times \frac{9}{10})<\frac{9}{10}$

Hence, we can clearly see that the value of the product of the proper fractions, i.e., $\frac{4}{5}\times \frac{9}{10}$ is less than the individual values of the proper fractions, i.e., $\frac{4}{5}$ and $\frac{9}{10}.$

Therefore, option (b.) is the correct answers.

$\underset{–}{\text{Note:}}$
The value of proper fraction lies between $0$ and $1$. If we multiply values, which are in-between $0$ and $1$, we get the product as less than the individual fractional values. And, this confirms that the multiplicative value of the proper fractions is less than the individual proper fractions.