Question

What is the quotient of $\dfrac{3}{4}$ divided by $\dfrac{7}{8}$ ?

Answer 1

Hint: Here we have to carry out division between two fractions. To carry out division between two fractions, first we need to take the reciprocal of the second fraction and then change the division sign to multiplication sign. Then multiply the two fractions and we will get our answer.

Complete step by step solution:
In this question, we are given two fractions and we have to divide them and find their quotient.
The number which is being divided is known as dividend and the number which divides the dividend is known as the divisor.
Here, our dividend is $\dfrac{3}{4}$ and the divisor is $\dfrac{7}{8}$ and we have to find the quotient.
Now, the given two numbers are fractions and fractions cannot be directly divided.
First of all we will take the reciprocal of the second number.
Reciprocal means writing denominator in numerator and writing numerator in denominator.
So, reciprocal of $\dfrac{7}{8}$$ = \dfrac{8}{7}$.
Now, we will change the operation sign.
As we have taken reciprocal, we have to change the division sign to multiplication sign.
So, now we have to multiply these two fractions.
$\Rightarrow \dfrac{3}{4} \div \dfrac{7}{8} = \dfrac{3}{4} \times \dfrac{8}{7}$
Now, two times 4 is 8. So, we cancel them out in the above equation. Therefore,
$\Rightarrow \dfrac{3}{4} \div \dfrac{7}{8} = \dfrac{3}{4} \times \dfrac{8}{7} = \dfrac{3}{1} \times \dfrac{2}{7} = \dfrac{6}{7}$
Therefore, we have divided $\dfrac{3}{4}$ by $\dfrac{7}{8}$ and got the answer $\dfrac{6}{7}$.
Hence, the quotient of $\dfrac{3}{4}$ divided by $\dfrac{7}{8}$ is $\dfrac{6}{7}$.

Note:
We can also find the quotient of $\dfrac{3}{4}$ divided by $\dfrac{7}{8}$ in decimal form.
First of all, divide 3 by 4 and then divide 7 by 8.
$\Rightarrow \dfrac{3}{4} = 0.75,\dfrac{7}{8} = 0.875$
Now, divide $0.75$ by $0.875$.
$\Rightarrow 0.75 \div 0.875 = 0.85714$
$\Rightarrow \dfrac{6}{7} = 0.85714$
Hence, both the answers are the same.