ADDITION OF MIXED FRACTION -
To add mixed fractions (fractions with both a whole number and a fraction), you can follow these steps:
Steps to Add Mixed Fractions:-
1. Convert the Mixed Fractions to Improper Fractions:-
Multiply the whole number by the denominator and add the numerator.
2 (3 × 5) + 2 (15 + 2) 17
Example.1) 3 ------ = ------------- = ---------- = --------
5 5 5 5
2. Find a Common Denominator (if needed):-
If the fractions have different denominators, find the least common multiple (LCM) and adjust the fractions to have this common denominator.
3. Add the Fractions:-
Add the numerators, keeping the common denominator.
4. Convert Back to a Mixed Number (if needed):-
If the result is an improper fraction, convert it back to a mixed number.
1 1
Example:- Add 2 ------ & 3 -------
4 3
Ans.)
Step.1) Convert to improper fractions:-
1 (2 x 4) + 1 (8 + 1) 9
2 ------ = -------------- = ---------- = -------
4 4 4 4
1 (3 x 3) + 1 (9 + 1) 10
3 -------- = ------------- = ---------- = -------
3 3 3 3
Step.2) Find a common denominator:-
9 10
---------, --------- [The LCM of 4 and 3 is 12.]
4 3
Adjust the fractions:-
9 (9 x 3) 27
--------- = ------------ = -------
4 (4 x 3) 12
10 (10 x 4) 40
------- = ----------- = -------
3 (3 x 4) 12
Step.3) Add the fractions:-
27 40 (27 + 40) 67
-------- + -------- = ------------ = -------
12 12 12 12
Step.4) Convert back to a mixed number:-
67 7
------- = 5 -------
12 12
Final Answer:-
1 1 7
2 ------- + 3 ------- = 5 ------- (Ans.)
4 3 12
Another Way Of Solving the Same Problem:-
1 1
Example:- Add 2 ------ & 3 -------
4 3
Ans.) 1 1
2------ + 3------
4 3
1 1
=> (2 + 3) + (------ + ------) Step.1 Add the Whole number
4 3
L.C.M of denominator 4 & 3 is 12
1 x 3 1 x 4
=> 5 + (------- + -------) Step.2 To add them convert into like fraction
4 x 3 3 x 4
3 4
=> 5 + (------ + ------)
12 12
7
=> 5 + ------- Step.3 Add the addition of whole number & like fraction
12
7
=> 5 ------ (Ans.)
12