Question

What is $\dfrac{3}{4}$ divided by $\dfrac{3}{8}$?

Answer 1

Hint: To solve this kind of question, we need to know about basic concepts like fractions and decimal form. Here we can solve the question in fraction form and decimal form. We will perform the division of the given fractions by using the concepts of reciprocals to convert it into a single fraction. Then we will simplify to get the answer.

Complete step by step solution:
Fraction is defined as it represents any number with equal parts in a set of whole numbers.
It is represented in the form of ‘/’, for example a/b. The number on the top is known as ‘numerator’, and the number below is called ‘denominator’. There are 6 different types of fractions namely proper fractions, improper ,like, unlike and mixed fractions.
Here the given question is $\dfrac{3}{4}$ divided by $\dfrac{3}{8}$ ,which is mathematically written as,
i.e., \[\dfrac{3}{4}\div \dfrac{3}{8}\].
The numbers on the left-hand side of division symbol i.e., $\dfrac{3}{4}$ are labelled as
3=dividend numerator
4=dividend denominator
The numbers on the left-hand side of division symbol i.e., $\dfrac{3}{8}$ are labelled as
3= divisor numerator
8=divisor denominator
To make answer it in a fraction form, we need to multiply the dividend denominator by divisor numerator to make a new denominator
\[\Rightarrow \dfrac{3 \times 8}{4 \times 3}\]
\[\Rightarrow \dfrac{24}{12}\Rightarrow \dfrac{2}{1}\]
Thus, the answer to $\dfrac{3}{4}$ divided by $\dfrac{3}{8}$ in fraction form is $\dfrac{2}{1}$ or simply $2$.

Note: The common mistake done in the fractions concept is believing that fractions’ numerators and denominators should be managed as a set of whole numbers. Most of the mistakes happen here. Students leave the denominator unchanged in fraction multiplication problems. And also failing to understand the reciprocate-and multiply procedure for solving fraction-based division problems. To answer the given problem in decimal form, we need to simply divide the numerator by the denominator from the fraction:
$\dfrac{3}{4} = 0.75$ and $\dfrac{3}{8} = 0.375$
\[\Rightarrow \dfrac{0.75}{0.375}\]
\[\Rightarrow 2\]
Whether the solving method is fraction form or decimal form, the answer for the given fractions is the same.