Question

What is $ \dfrac{3}{4} $ divided by $ \dfrac{4}{7}? $

Answer 1

Hint: As we can see that we have given fractions and we have to divide that. We know that a fraction is a part of the whole number and it consists of two parts- numerator and denominator. Let us take a fraction $ \dfrac{a}{b} $ , we can say that $ a $ , the upper part is the numerator and the lower part i.e. $ b $ is the denominator. We can say that dividing the fractions is division of fraction or as same as multiplying the fraction by the reciprocal which is the inverse of the other fraction.

Complete step-by-step answer:
Here we have $ \dfrac{3}{4} $ divided by $ \dfrac{4}{7} $ .
We know that the simple step of division of fraction is by converting it into multiplication of fraction.
Let the first fraction be $ \dfrac{3}{4} $ and the second fraction be $ \dfrac{4}{7} $ .
We can reciprocate the second fraction by interchanging its numerator with denominator and vice-versa. So the reciprocal of the second denominator is $ \dfrac{7}{4} $ .
Now we can multiply the second fraction with the first one by multiplying the numerators and denominators with each other.
So we can write $ \dfrac{3}{4} \times \dfrac{7}{4} = \dfrac{{21}}{{16}} $ .
Hence the required answer is $ \dfrac{{21}}{{16}} $ .
So, the correct answer is “ $ \dfrac{{21}}{{16}} $ ”.

Note: We should remember that with fractions we can change a division into multiplication by flipping the second fraction i.e. $ \dfrac{3}{{\dfrac{4}{{\dfrac{4}{7}}}}} $ can be written as $ \dfrac{3}{4} \times \dfrac{1}{{\dfrac{4}{7}}} $ , again it can be written as $ \dfrac{3}{4} \times \dfrac{7}{4} $ .
Also we should know that if $ \dfrac{a}{b} $ is to be divided by $ c $ , then we can solve it as $ \dfrac{a}{b} \div \dfrac{c}{1} = \dfrac{a}{b} \times \dfrac{1}{c} $ . This is called dividing the fraction by the whole number.