Question

How is the process of multiplying fractions different from the process of adding fractions?

Answer 1

Hint: A fraction is defined as the ratio of two numbers and is represented as \[\dfrac{a}{b}\]. Multiplication and addition are the basic mathematical operation which helps to simplify a mathematical expression. Multiplication is used to find the product of two or more numbers whereas addition is used to combine two or more numbers or values.

Complete Step by Step Solution:
A fraction has two parts namely numerator and denominator.
Now while adding two or more fractions:
We must have the same denominator for both the fractions. When we have the same denominators then the numerator can be just added and then if possible it can be converted into its simplest form. Thus, the result of the addition of fractions has the numerator as the sum of the numerators of both the fractions and has the same denominator as both the fractions.
If the denominator of fractions is not the same then we take the LCM and first make the denominator the same. Then we will apply the above process to find the sum of two or more fractions.
Thus, adding the fractions can be represented as \[\dfrac{a}{b} + \dfrac{c}{b} = \dfrac{{a + c}}{b}\].
Example: Find the sum of \[\dfrac{1}{3}\] and \[\dfrac{4}{3}\].
\[\dfrac{1}{3} + \dfrac{4}{3} = \dfrac{5}{3}\]
For multiplying fractions:
When multiplying the fractions it is not necessary for us to have the same denominator for both the fractions. When we are multiplying the fractions, then the numerators can be multiplied and the denominators can be multiplied and then if possible it can be converted into its simplest form. Thus, the result of the product of fractions has the numerator as the product of the numerators and the denominator as the product of the denominators.
Thus, multiplying the fractions can be represented as \[\dfrac{a}{b} \cdot \dfrac{c}{d} = \dfrac{{a \cdot c}}{{b \cdot d}}\].
Example: Find the product of \[\dfrac{1}{2}\] and \[\dfrac{3}{4}\].
\[\dfrac{1}{2} \cdot \dfrac{3}{4} = \dfrac{3}{8}\]

Therefore, the Addition of fractions can be done only for like fractions whereas the Multiplication of fractions can be done for both the like and unlike fractions.

Note:
We know that a like fraction is defined as the fraction which has the same fractions and an unlike fraction is defined as a fraction which has different denominators. We should be careful when adding the unlike fractions, we should convert the unlike fractions into like fractions by finding the LCM of the denominators and then we will follow the process of addition of like fractions. There is no such rule for multiplying two fractions.