Question

How do you find the quotient of $${\displaystyle \frac{3}{7}}$$ divided by $${\displaystyle \frac{5}{8}}$$?

Answer 1

Hint: In the given question, we have been given an expression which has two fractions separated by a division sign. We have to simplify them. We can do that by changing the division sign into a multiplication sign and making just one necessary change to the fraction on the right side of the division sign. Then we multiply them and simplify to find the answer.

Formula Used:
Let there be two numbers $$a$$ and $$b$$. Then,
$$a÷b=a\times {\displaystyle \frac{1}{b}}$$

Complete step-by-step answer:
The given expression is $$p={\displaystyle \frac{3}{7}}÷{\displaystyle \frac{5}{8}}$$.
To solve that, we change the division sign into a multiplication sign by taking the reciprocal of the second fraction.
Hence,
$$p={\displaystyle \frac{3}{7}}\times {\displaystyle \frac{8}{5}}={\displaystyle \frac{24}{35}}$$

Note: In the given question, we had to divide two fractions. To do that, we change the division sign between the two fractions into multiplication. This is done by taking the reciprocal of the fraction on the right side of the division sign. Then we solve the two fractions by multiplying them, simplify them into lowest form, change the mixed fraction into improper fraction, and that gives us the answer.