ADDITION OF RATIONAL NUMBER WITH DIFFERENT DENOMINATOR -
When adding rational numbers with different denominators, you'll need to find a common denominator before adding the fractions. To do this, you can find the least common multiple (LCM) of the denominators and use it as the new denominator for both fractions. Then, you can convert each fraction to an equivalent fraction with the new denominator and add the numerators. Finally, simplify the result if possible.
We will learn the addition of rational number with different denominator. To find the sum of two rational numbers which do not have the same denominator, we follow the following steps:
Step I:- Let us obtain the rational numbers and see whether their denominators are positive or not. If the denominator of one (or both) of the numerators is negative, re-arrange it so that the denominators become positive.
Step II:- Obtain the denominators of the rational numbers in step I.
Step III:- Find the lowest common multiple of the denominators of the two given rational numbers.
Step IV:- Express both the rational numbers in step I so that the lowest common multiple of the denominators becomes their common denominator.
Step V:- Write a rational number whose numerator is equal to the sum of the numerators of rational numbers obtained in step IV and denominators is the lowest common multiple obtained in step III.
Example.1) Find the sum: −5/6 + 4/9
Solution:
The denominators of the given rational numbers are 6 and 9 respectively. LCM of 6 and 9 = (3 × 2 × 3) = 18.
Now, −5/6 = {(−5)×3}/(6×3) = −15/18
and 4/9 = (4×2)/(9×2) = 8/18
Therefore, −5/6 + 4/9
= −15/18 + 8/18
= (−15+8)/18
= −7/18 (Ans.)
2 1
Example.2) Add -------- & --------
3 4
When adding fractions, follow these steps:
Denominator of fractions are 3 & 4.
LCM of both the denominator is 3 X 4 = 12
2. Convert fractions to have the same denominator:- Rewrite each fraction so they have the common denominator found in step 1.
3. Add the numerators:- Once the fractions have the same denominator, add the numerators together.
4. Simplify the result (if necessary):- If possible, simplify the fraction by reducing it to lowest terms.
2 1
----------- + -----------
3 4
(2 X 4) (1 X 3)
= ---------------- + -----------------
(3 X 4) (4 X 3)
8 3
= ----------- + -----------
12 12
(8 + 3)
= ---------------
12
11
= ----------- (Ans.)
12
3 7
Example.3) Add ----------- and -----------
10 20
When adding fractions, follow these steps:
Denominator of fractions are 10 & 20.
LCM of both the denominator is 10 X 20 = 20
2. Convert fractions to have the same denominator:- Rewrite each fraction so they have the common denominator found in step 1.
3. Add the numerators:- Once the fractions have the same denominator, add the numerators together.
4. Simplify the result (if necessary):- If possible, simplify the fraction by reducing it to lowest terms.
3 7
------------ + -----------
10 20
(3 X 2) (7 X 1)
= ---------------- + ---------------
(10 X 2) (20 X 1)
6 7
= ----------- + -----------
20 20
13
= ------------ (Ans.)
20