Question

Aneeta bought \[3\dfrac{1}{4}\] kg apples and \[4\dfrac{1}{2}\] kg guava. What is the total weight of fruits purchased by her?

Answer 1

Hint: Whenever we need to find out the total value of some goods the operation we perform is addition. For addition of unlike fractions (having different denominators). At first, we take the LCM of denominators and then add the fractions by making them equivalent fractions. For converting whole fraction into improper fraction at first multiply denominator with whole part and then add the numerator to it.

Complete step-by-step solution:
Aneeta bought two types of fruits, i.e., apples and guava. The total weight of fruits bought by her will be equal to the sum of the weights of apples and guavas. So, at first, we will convert the fractions of both into improper fractions and then we will add them together by taking LCM.
Weight of Apples bought by Aneeta = \[3\dfrac{1}{4}\]kg = \[\dfrac{{13}}{4}\]kg
Weight of Guava bought by Aneeta = \[4\dfrac{1}{2}\] kg = \[\dfrac{9}{2}\]
Total weight of fruits bought by Aneeta = \[\dfrac{{13}}{4}\]kg + \[\dfrac{9}{2}\]kg
The LCM of the dynameters (4 and 2) is 2. Thus,
 = \[\dfrac{{13 + 9(2)}}{4}\] kg (LCM of $4$ and $2$ is $4$)
We first need to know about the LCM, which is the least common multiple of the given numbers, we will find its common multiple and then convert it into the prime factor multiple and finally take the least among them.
= \[\dfrac{{13 + 18}}{4}\]kg
 = \[\dfrac{{31}}{4}\]kg
= \[7\dfrac{3}{4}\]kg
The total weight of fruits bought by Aneeta = \[7\dfrac{3}{4}\] kg.

Note: Take proper care while calculating LCM and converting the whole fraction into improper and vice versa. While calculating the LCM by using prime factorization method use only prime factors.
The LCM stands for Least common multiple or lowest common multiple. The LCM of a number is the smallest number that is the product of two or more than two numbers. There is more than one method to find the LCM. The quickest way is using the prime factors of each number and then producing the least powers of the common prime factors.