Question

How do you write $ 3\dfrac{3}{4} $ as an improper fraction?

Answer 1

Hint:
A fraction in which the numerator is greater than the denominator is called an improper fraction. Since $ 3\dfrac{3}{4} $ is a mixed fraction, it can be converted into an improper fraction. In order to do this, just add the whole part to the fractional part, to get a single fraction. Remember that we can add fractions when they have the same denominators.

Complete Step by step Solution:
We know that a mixed fraction $ 3\dfrac{3}{4} $ means a value of 3 + $ \dfrac{3}{4} $ , which can also be written as $ \dfrac{3}{1} $ + $ \dfrac{3}{4} $ .
In order to equate the denominators, let's multiply both the numerator and the denominator of the first fraction by 4, to get:
= $ \left( \dfrac{3}{1}\times \dfrac{4}{4} \right) $ + $ \dfrac{3}{4} $
= $ \dfrac{12}{4} $ + $ \dfrac{3}{4} $
Adding the numerators, we get:

= $ \dfrac{15}{4} $, which is the required improper fraction.

Note:
There are two common types of fractions: Proper and improper. A proper fraction is the one in which the numerator is smaller than the denominator.
Improper fractions can be written as a mixed fraction $ a\dfrac{b}{c} $ , with a whole part 'a' and a fractional part $ \dfrac{b}{c} $ added together.
When representing the numbers, for radical numbers $ a\sqrt{b} $ means "a × $ \sqrt{b} $ ", whereas for fractions $ a\dfrac{b}{c} $ means "a + $ \dfrac{b}{c} $ ".