Name: Introduction to Equivalent Fractions
Uploaded: 2019-07-19
Duration: 4 min 45 s
Description: You are already familiar with the fractions used to represent the part of the whole thing. But do you know what equivalent fractions are? Let us watch this video to find out.

Question

Find the product of

\frac{1}{4}

and

\frac{8}{5}

and show that it is less than

\frac{8}{5}

but more than

\frac{1}{4}

.

Accepted Answer

We have, $\frac{1}{4} \times \frac{8}{5} = \frac{1 \times 8}{4 \times 5}$ [The product of two fractions $= \frac{Product of the numerators}{Product of the denominators}$ ]

$= \frac{1 \times 2 \times 4}{4 \times 5} = \frac{2}{5}$ .

Clearly, $\frac{2}{5}$ is $\frac{8}{5}$ because the denominators of both fractions remaining the same $(5)$ , the numerator $2$ of $\frac{2}{5}$ is lesser than the numerator $8$ of $\frac{8}{5}$ .

Now, we have to compare $\frac{2}{5}, \frac{8}{5}$ and $\frac{1}{4}$ .

For this, we shall convert the fractions into their equivalent fractions such that the denominators of all of them are equal to their LCM. Then, we shall compare the numerators. The fraction with the greater numerator is greater.

The LCM of $5, 5$ and $4$ is $20$ .

Thus, we have, $\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}$ , $\frac{8}{5} = \frac{8 \times 4}{5 \times 4} = \frac{32}{20}$ and $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$ .

Comparing the numerators, we observe, $5 < 8 < 32$ .

Thus, we have, $\frac{5}{20} < \frac{8}{20} < \frac{32}{20}$ or $\frac{1}{4} < \frac{2}{5} < \frac{8}{5}$ .

Therefore, the product is less than $\frac{8}{5}$ , but more than $\frac{1}{4}$ .

Find the product of $\frac{1}{4}$ and $\frac{8}{5}$ and show that it is less than $\frac{8}{5}$ but more than $\frac{1}{4}$ .

Important Questions on Fractions

Learn and Prepare for any exam you want !

Find the product of 14 and 85 and show that it is less than 85 but more than 14.

Important Questions on Fractions

Learn and Prepare for any exam you want !

Find the product of $\frac{1}{4}$ and $\frac{8}{5}$ and show that it is less than $\frac{8}{5}$ but more than $\frac{1}{4}$ .