Question

How do you figure out this fraction? \[\dfrac{1}{2} + \dfrac{1}{4} = \]

Answer 1

Hint: Fraction represents the portion of a whole or of a collection. Fractions can be of two types:- Like fractions and Unlike fractions
Like fractions are those whose denominator is greater than numerator and unlike fractions are those whose denominator is smaller than numerator. So unlike fractions can be converted to mixed fractions. Mixed fraction is simply an improper fraction written as the sum of a whole number and a proper fraction.
To get the sum of two such fractions, we need to get the L.C.M. of the denominators and convert the fractions into equivalent fractions with the same denominator. After that we just need to add the numerators of the final equivalent fractions to get the final result.

Complete step-by-step answer:
Given fractions are \[\dfrac{1}{2}\] and \[\dfrac{1}{4}\] , which are like fractions.
So, at first we need to find the L.C.M. of \[2\] and \[4\] .
L.C.M. ( Least Common Multiple) is the method to find the smallest possible multiple of two or more numbers.
To find the LCM of \[2\] and \[4\] , we need to find the multiples of \[2\] and \[4\] .
Multiples of \[2\] :- \[2,4,6,8,10\]
Multiples of \[4\] :- \[4,8,12,16,20\]
So now we have to choose the smallest multiple which is exactly divisible by \[2\] and \[4\] and on observing the both multiples of \[2\] and \[4\] , we choose \[4\] as the smallest multiple which is exactly divisible by \[2\] and \[4\] . Hence the L.C.M. of \[2\] and \[4\] is \[4\] .
Now we have to convert the given fractions into equivalent fractions so that both of them have the same denominator.
Multiplying \[2\] with both numerator and denominator of \[\dfrac{1}{2}\] , we get,
 \[\dfrac{{1 \times 2}}{{2 \times 2}} = \dfrac{2}{4}\]
and multiplying \[1\] with both numerator and denominator of \[\dfrac{1}{4}\] , we get,
 \[\dfrac{{1 \times 1}}{{4 \times 1}} = \dfrac{1}{4}\]
So the equivalent fractions are \[\dfrac{2}{4}\] and \[\dfrac{1}{4}\] .
Now we have to add the numerator of these two equivalent fractions to get the final result,
 \[\therefore \dfrac{2}{4} + \dfrac{1}{4} = \dfrac{{2 + 1}}{4} = \dfrac{3}{4}\]
Hence on adding \[\dfrac{1}{2}\] and \[\dfrac{1}{4}\] , we get \[\dfrac{3}{4}\] .
So, the correct answer is “ \[\dfrac{3}{4}\]”.

Note: Fraction represents the portion of a whole or of a collection. Fractions generally have two parts: Numerators and Denominators. The numerator is the integer written on the top which usually indicates the number of parts that we have selected out of the total number of equal parts whereas the denominator is the integer written on the bottom indicating the total number of equal parts. Be careful in calculating the L.C.M. of the denominators and then in converting to equivalent fraction. Be sure of the integer which needs to be multiplied with the fraction to get the equivalent fraction with the same denominators