How do you divide $2\dfrac{5}{7}\div 3\dfrac{5}{8}$ ?

Hint:The divisor and dividend in $2\dfrac{5}{7}\div 3\dfrac{5}{8}$ is mixed fraction. First, we have to convert both the mixed fraction to simple fraction. $2\dfrac{5}{7}$ is equal to $\dfrac{19}{7}$ and $3\dfrac{5}{8}$ is equal to $\dfrac{29}{8}$ . We know that fraction a divided by fraction b is equal to a multiplied by reciprocal of b. To find reciprocal of any fraction, we can just alternate denominator and numerator. When we multiply 2 fractions, we can just simply multiply the numerator and denominator.

Complete step by step answer:
We have to solve $2\dfrac{5}{7}\div 3\dfrac{5}{8}$
Let’s convert $2\dfrac{5}{7}$ and $3\dfrac{5}{8}$ to a simple fraction. $2\dfrac{5}{7}$ is equal to $\dfrac{19}{7}$ and $3\dfrac{5}{8}$ is equal to $\dfrac{29}{8}$
$\Rightarrow 2\dfrac{5}{7}\div 3\dfrac{5}{8}=\dfrac{19}{7}\div \dfrac{29}{8}$
We know that fraction a divided by fraction b is equal to a multiplied by reciprocal of b
Reciprocal of $\dfrac{29}{8}$ is equal to $\dfrac{8}{29}$
$2\dfrac{5}{7}\div 3\dfrac{5}{8}$ is equal to multiplication of $\dfrac{19}{7}$ and $\dfrac{8}{29}$
$\Rightarrow 2\dfrac{5}{7}\div 3\dfrac{5}{8}=\dfrac{19}{7}\times \dfrac{8}{29}$
Now we can just multiply numerator and denominator
$\Rightarrow 2\dfrac{5}{7}\div 3\dfrac{5}{8}=\dfrac{152}{203}$
$\dfrac{152}{203}$ is the quotient when we divide $2\dfrac{5}{7}$ by $3\dfrac{5}{8}$

Note:
When we divide fraction a by fraction b , if fraction b is an integer then we can take the denominator is equal to 1. Always remember that we can make denominators of a fraction 0 and we can not divide any number by 0. So the numerator of the divisor can not be 0. We can not find the reciprocal of 0. The reciprocal of 0 tends to infinity. We know that the product of any number and its reciprocal is equal to 1. There is no real number such that the product of the number and 0 is equal to 1.