CLASS-5
ADDITION OF FRACTION
Addition Of Fractions -
When you are adding two or more fractions, first change all the fractions to their equivalent fractions with common denominator (which is the L.C.M. of the denominators of the fractions) and then add.
To add fractions, you need to have a common denominator. The common denominator is the least common multiple of the denominators of the fractions being added.
Once you have a common denominator, you can add the numerators of the fractions and simplify the resulting fraction, if necessary.
Here are the steps to add two fractions:
- Find the least common multiple (LCM) of the denominators.
- Rewrite each fraction with the common denominator.
- Add the numerators of the fractions.
- Simplify the resulting fraction, if necessary.
For example, let's say you want to add 1/4 and 2/3:
- The least common multiple of 4 and 3 is 12.
- Rewrite 1/4 and 2/3 with a denominator of 12: 1/4 = 3/12, 2/3 = 8/12.
- Add the numerators: 3/12 + 8/12 = 11/12
- The resulting fraction is already in its simplest form, so the answer is 11/12.
So, 1/4 + 2/3 = 11/12.
Example.1) Add the following fractions:
4 3 1
------- + ------- + -------
5 10 20
Ans.)
4 3 1
------- + ------- + -------
5 10 20
To add, first I need to find LCM of denominator of given fraction
Now we will divide the obtained LCM by each denominator of each fraction one by one, and then multiply the obtained quotient to denominator and numerator of the fraction to convert equivalent fraction.
4 4 X 4 16
------- = ---------- = -------
5 5 X 4 20
3 3 X 2 6
------- = ---------- = ------
10 10 X 2 20
1 1 X 1 1
------- = ----------- = -------
20 20 X 1 20
4 3 1
------- + ------- + -------
5 10 20
{(20 ÷ 5) X 4} + {(20 ÷ 10) X 3} + {(20 ÷ 20) X 1}
= -----------------------------------------------
20
(4 X 4) + (3 X 2) + (1 X 1)
= ---------------------------
20
16 + 6 + 1
= -------------
20
23
= ----------- (Ans.)
20
Example.2) Add the following fractions:
1 3 3
2 ----- + 3 ----- + 2 ------
2 5 10
Ans.)
1 3 3
2 ------- + 3 ------- + 2 -------
2 5 10
First convert the mixed numbers into improper fractions.
5 18 23
------- + ------- + -------
2 5 10
{(10 ÷ 2) X 5} + {(10 ÷ 5) X 18} + {(10 ÷ 10) X 23}
= -------------------------------------------------
10
(5 X 5) + (2 X 18) + (1 X 23)
= ------------------------------
10
(25 + 36 + 23)
= ------------------
10
84 42 2
= -------- = ------ = 8 ------- (Ans.)
10 5 5