Question

Find: $14÷{\displaystyle \frac{5}{6}}$

Answer 1

Hint: We use laws of number systems to get the value.

Complete Step by Step solution:

We have $14÷{\displaystyle \frac{5}{6}}=$${\displaystyle \frac{84}{5}}$
We know that whenever in finding value there is a division we convert division to multiplication by taking reciprocal of divisor. Here divisor is ${\displaystyle \frac{5}{6}}$

We can write given equation as $14\times {\displaystyle \frac{6}{5}}$

Now, we will do the simplification like cancellation if possible if not then multiplying numerator with numerator and denominator with denominator to get a single rational number.

As, there is no cancellation possible in numerator and denominator.
Therefore, we have ${\displaystyle \frac{84}{5}}$

Here, is an improper fraction as its numerator is greater than that of the denominator. Hence, we write it as a mixed fraction.

On dividing $84$ by $5$ we will get $16$ as quotient and $4$ as of remainder. Therefore a mixed fraction of ${\displaystyle \frac{84}{5}}$ is $16{\displaystyle \frac{4}{5}}$.
Hence, the required value of $14÷{\displaystyle \frac{5}{6}}$ is $16{\displaystyle \frac{4}{5}}$.

Note: We should be very careful while doing calculations and also express improper fraction to mixed fraction.