Question

Solve the equation:
$2\dfrac{3}{4} \div 2\dfrac{2}{3} \div \dfrac{1}{2} = ?$

Answer 1

Hint: we can simplify this question by putting the brackets around each fraction. We have to do it step by step to get the correct answer. In this question, if we do the reciprocal of a number then the divide sign will get converted into multiply. Before doing any calculation convert the mixed fraction into an improper fraction.

Complete step by step answer:
$ = \,2\dfrac{3}{4} \div 2\dfrac{2}{3} \div \dfrac{1}{2}$
Now put the brackets around each fraction,
$ = \left( {2\dfrac{3}{4} \div \left( {2\dfrac{2}{3} \div \left( {\dfrac{1}{2}} \right)} \right)} \right)$
Convert the mixed fractions into improper fractions,
$ = \left( {\dfrac{{11}}{4} \div \left( {\dfrac{8}{3} \div \left( {\dfrac{1}{2}} \right)} \right)} \right)$
Now, the multiplicative inverse of $\dfrac{1}{2}$ is $2$ and the divide sign will convert into multiply.
$ = \left( {\dfrac{{11}}{4} \div \left( {\dfrac{{16}}{3}} \right)} \right)$
Again, we do the multiplicative inverse of $\dfrac{{16}}{3}$ and it’s get converted into $\dfrac{3}{{16}}$ and the divide sign will get converted into multiply.
$ = \left( {\dfrac{{11}}{4} \times \dfrac{3}{{16}}} \right)$
On multiplication, we get
$ = \dfrac{{33}}{{64}}$

Note:
Do this question step by step. Otherwise, you will get confused about how to solve this question. One must also know the meaning of reciprocal. The meaning of reciprocal is the inverse of any number. In this question, we have used the term multiplicative inverse which means the same as the reciprocal of a number.