Question

How do you simplify $\dfrac{3}{4} \div \dfrac{1}{8}$?

Answer 1

Hint: We are given the numbers in fraction form. We have to divide the fractions. To divide the fractions, first, reciprocate the second fraction and replace the division operation with the multiplication operation. Then, simplify the fraction by canceling out the common terms. Then, write the result in simplified form.

Complete step by step solution:
We are given the expression, $\dfrac{3}{4} \div \dfrac{1}{8}$.

Now, reciprocate the second fraction by interchanging the numerator and denominator.

The fraction $\dfrac{1}{8}$ can be written as $\dfrac{8}{1}$ after interchanging.

 Now, we will replace the division symbol with a multiplication sign.

$ \Rightarrow \dfrac{3}{4} \div \dfrac{1}{8} = \dfrac{3}{4} \times \dfrac{8}{1}$

Now, we will cancel out the common terms, to simplify the expression.

$ \Rightarrow \dfrac{3}{{{4}}} \times \dfrac{{{8}}}{1} = 3 \times 2$

Multiply the terms to write the expression in simplified form.

$ \Rightarrow 3 \times 2 = 6$

Now, the term cannot be simplified further.

Hence, the value of $\dfrac{3}{4} \div \dfrac{1}{8}$ is $6$.

Note: The students must note that in such types of questions, the process of reciprocating the fraction will change the sign from division to multiplication because the inverse of multiplication is division. So, the division of fractions is equivalent to multiplying the fractions by the reciprocal or the inverse of the other fraction.

Students, please note that this question can be also solved using the first principle of division described here. In this method, we will make the denominators the same by multiplying and dividing the first fraction by 2.

$ \Rightarrow \dfrac{{3 \times 2}}{{4 \times 2}} \div \dfrac{1}{8} = \dfrac{6}{8} \div \dfrac{1}{8}$

Now, since the denominator of both fractions are the same, then the result of division of $8 \div 8 = 1$. Thus, the denominator becomes 1.

Now, we will divide the numerators.

$ \Rightarrow \dfrac{{6 \div 1}}{1} = 6$

Therefore, the answer using this method is the same as 6.