What is $2\dfrac{1}{7}\div 2\dfrac{1}{2}?$

Hint: We are required to simplify the expression involving fractions. We first convert these mixed fractions into improper fractions. We then divide the given fractions. We know that division by a number is the same as multiplication by the reciprocal of that number. Using this, we solve the given question by cancelling the common factors.

Complete step by step solution:
The given question requires us to simplify $2\dfrac{1}{7}\div 2\dfrac{1}{2}.$ We first convert these mixed fractions to improper fractions. We need to know the method to do this. Converting the first mixed fraction into an improper fraction,
$\Rightarrow 2\dfrac{1}{7}=\dfrac{7\times 2+1}{7}$
Multiplying 7 and 2 in the numerator and adding with 1,
$\Rightarrow 2\dfrac{1}{7}=\dfrac{15}{7}$
Next, we convert the second mixed fraction to an improper form,
$\Rightarrow 2\dfrac{1}{2}=\dfrac{2\times 2+1}{2}$
Multiplying 2 and 2 in the numerator and adding with 1,
$\Rightarrow 2\dfrac{1}{2}=\dfrac{5}{2}$
Now we rewrite the equation given in the question as $2\dfrac{1}{7}\div 2\dfrac{1}{2}$ by replacing them with their improper fraction forms,
$\Rightarrow \dfrac{15}{7}\div \dfrac{5}{2}$
We know that division of two numbers is the same as the first number multiplied by the reciprocal of the second number. Therefore, we convert this to multiplication by reciprocating the second fraction.
$\Rightarrow \dfrac{15}{7}\times \dfrac{2}{5}$
We now check for common factors to simplify the above expression. We know the HCF of 15 and 5 is 5. Therefore, we cancel them out and see that no further simplification by cancelling factors is possible.
$\Rightarrow \dfrac{3}{7}\times \dfrac{2}{1}$
Multiplying the numerators and denominators separately and writing,
$\Rightarrow \dfrac{6}{7}$

This is already in a proper fraction form. Hence, $2\dfrac{1}{7}\div 2\dfrac{1}{2}$ results in $\dfrac{6}{7}.$

Note: It is important to know how to convert the mixed fractions into an improper fraction form and vice versa. To convert the mixed fraction to an improper fraction, we multiply the whole number with the denominator and add the result to the numerator and this becomes the new numerator term. The denominator remains the same. To convert from improper fractions to mixed fractions, we need to divide the numerator by the denominator and the quotient obtained is written as a whole number and the remainder becomes the numerator. The denominator remains the same in this case too.