Question

How do you solve $20\dfrac{1}{2} \div \dfrac{3}{4}$

Answer 1

Hint:Start by defining the terms improper fraction and mixed fractions. First, we will reduce the fractional part.
Then we will convert the mixed number to an improper fraction. Reduce the fractional
part until it cannot be done any further and then mention the final fraction.

Complete step by step answer: First we will start by reducing the fractional part $\dfrac{1}{2}$ . As we can see the fractional part cannot be reduced any further so we will proceed further. Now we will convert the mixed number $20\dfrac{1}{2}$ into an improper fraction.
We will multiply the denominator by the whole number part and the numerator. By doing this we will get a new numerator. Now place the new numerator that is $41$ over the old denominator.
So, the final fraction will be $\dfrac{{41}}{2}$.
Now the expression becomes, $\dfrac{{41}}{2} \div \dfrac{3}{4}$.
Now we will multiply the term by its reciprocal and then eventually cross cancel the terms.
$
= \dfrac{{41}}{2} \times \dfrac{4}{3} \\
= \dfrac{{41}}{1} \times \dfrac{2}{3} \\
= \dfrac{{82}}{3} \\
$
Hence, the value of the expression $20\dfrac{1}{2} \div \dfrac{3}{4}$ will be $\dfrac{{82}}{3}$
Additional Information: An improper fraction is a fraction in which the numerator is greater than orequal to the denominator. Improper fractions are just another way of writing a mixed number.
Improper fractions are usually easier to use than mixed fractions. But generally mixed numbers are used. A mixed number is a number consisting of a whole number and a proper fraction.

Note: While reducing make sure you reduce by forming factors. This way you won’t commit any mistakes. When converting a mixed number to an improper fraction make sure you follow the correct sequence while doing that.