Answer
Verified
428.4k+ views
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.
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.
Recently Updated Pages
10 Examples of Evaporation in Daily Life with Explanations
10 Examples of Diffusion in Everyday Life
1 g of dry green algae absorb 47 times 10 3 moles of class 11 chemistry CBSE
If the coordinates of the points A B and C be 443 23 class 10 maths JEE_Main
If the mean of the set of numbers x1x2xn is bar x then class 10 maths JEE_Main
What is the meaning of celestial class 10 social science CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In the tincture of iodine which is solute and solv class 11 chemistry CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE