Question

How do you divide $2\dfrac{5}{7}\div \dfrac{3}{2}$ ?

Answer 1

Hint: We have to divide $2\dfrac{5}{7}$ by $\dfrac{3}{2}$ . First, we have to convert the mixed fraction $2\dfrac{5}{7}$ to simple fraction. We know that fraction a divided by fraction b is equal to a multiplied by reciprocal of b. $2\dfrac{5}{7}$ is equal to $\dfrac{19}{7}$ and reciprocal of $\dfrac{3}{2}$ is equal to $\dfrac{2}{3}$ . When we multiply 2 fractions, we can just simply multiply the numerator and denominator.

Complete step by step answer:
We have to solve $2\dfrac{5}{7}\div \dfrac{3}{2}$
Let’s convert $2\dfrac{5}{7}$ to a simple fraction. $2\dfrac{5}{7}$ is equal to $\dfrac{19}{7}$
$\Rightarrow 2\dfrac{5}{7}\div \dfrac{3}{2}=\dfrac{19}{7}\div \dfrac{3}{2}$
We know that fraction a divided by fraction b is equal to a multiplied by reciprocal of b
Reciprocal of $\dfrac{3}{2}$ is equal to $\dfrac{2}{3}$
$\Rightarrow 2\dfrac{5}{7}\div \dfrac{3}{2}=\dfrac{19}{7}\times \dfrac{2}{3}$
Now we can just multiply numerator and denominator
$\Rightarrow 2\dfrac{5}{7}\div \dfrac{3}{2}=\dfrac{38}{21}$
If we want, we can convert $\dfrac{38}{21}$ into mixed fraction. $\dfrac{38}{21}$ is equal to $1\dfrac{17}{21}$ .
$\Rightarrow 2\dfrac{5}{7}\div \dfrac{3}{2}=1\dfrac{17}{21}$
$1\dfrac{17}{21}$ is the quotient when we divide $2\dfrac{5}{7}$ by $\dfrac{3}{2}$

Note:
When we divide fraction a by fraction b , then the denominator of both fraction should not be 0. And the numerator of the divisor should not be 0, because we can not divide anything by 0. When fraction b is an integer, we can assume the denominator is equal to 1. If the dividend is 0 then the quotient is always 0. If the numerator of a fraction is greater than the denominator, then we can convert the fraction into mixed fraction. If there is a common factor between numerator and denominator of a fraction, we can cancel that out.