Question

How do you write \[3\dfrac{1}{4}\] as an improper fraction?

Answer 1

Hint: An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. To write the given mixed number as an improper fraction, we need to multiply the whole number by the denominator of a fraction. Add that to the numerator and then write the obtained terms on top of the denominator, hence you get an improper fraction.

Complete step by step solution:
Given,
 \[3\dfrac{1}{4}\] , in which we need to write the given number as an improper fraction.
As, a mixed number is an addition of its whole and fractional parts i.e., add 3 and \[\dfrac{1}{4}\] :
 \[3 + \dfrac{1}{4}\]
To write 3 as a fraction with a common denominator, multiply by \[\dfrac{4}{4}\] as:
 \[ = 3 \cdot \dfrac{4}{4} + \dfrac{1}{4}\]
Combine 3 and \[\dfrac{4}{4}\] we get:
 \[ = \dfrac{{3 \cdot 4}}{4} + \dfrac{1}{4}\]
Combine the numerators over the common denominator as:
 \[ = \dfrac{{3 \cdot 4 + 1}}{4}\]
Simplify the numerator terms i.e., multiply 3 by 4 as:
 \[ = \dfrac{{12 + 1}}{4}\]
Our next step is to add the numerator terms, 12 and 1, giving us the desired improper fraction:
 \[ = \dfrac{{13}}{4}\]
So, the correct answer is “ \[ \dfrac{{13}}{4}\] ”.

Note: The fraction is defined as the ratio of two numbers and it is represented using the form \[\dfrac{x}{y}\] or numerator value with denominator value. Types of fraction are:
Proper Fraction: If the numerator value is smaller than the denominator value, then it is called a proper fraction.
Improper Fraction: If the numerator value is larger than the denominator value, then it is called an improper fraction.
Mixed Fraction: The mixed fraction is defined as the combination of a whole number and a proper fraction.
To convert a mixed fraction to an improper one, we must transfer the whole number into the numerator of the fraction. In an improper fraction, the numerator is greater than the denominator, hence note that improper fraction is always greater than one. A proper fraction has a numerator smaller than the denominator but an improper fraction has a denominator smaller than the numerator.