how to add rational numbers
Answers
Answer:
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Step-by-step explanation:
In addition we divide the rational numbers into the following two categories:
1. When Given Numbers have same Denominator:
In this case, we define (a/b + c/b) = (a + c)/b
For example:
(i) Add 3/7 and 56/7
Solution:
3/7 + 56/7
= (3 + 56)/7
= 59/7, [Since, 3 + 56 = 5 9]
Therefore, 3/7 + 56/7 = 59/7
(ii) Add 8/13 and -5/13
Solution:
3/13 + -5/13
= [3 + (-5)]/13
= (3 -5)/13
= -2/13, [Since, 3 - 5 = -2]
Therefore, 3/13 + -5/13 = = -2/13.
2. When Denominators of Given Numbers are Unequal:
In this case we take the (least common multiple) LCM of their denominators and express each of the given numbers with this LCM as the common denominator. Now, we add these numbers as shown above.
For example:
(i) Add 5/6 and 7/9
Solution:
Clearly, denominators of the given numerators are positive.
The LCM of the denominators 6 and 18 is 18.
Now, we express 5/6 and 7/9 into forms in which both of them have the same denominator 18.
We have,
5/6 = 5 × 3/6 × 3 = 15/18
and
7/9 = 7 × 2/9 × 2 = 14/18
Therefore, 5/6 + 7/9
= 15/18 + 14/18
= (15 + 14)/18
= 29/18
(ii) Add 5/6 and -3/7
Solution:
The denominators of the given rational numbers are 6 and 7 respectively.
The LCM of 6 and 7 is 42.
Now, we rewrite the given rational numbers into forms in which both of them have the same denominator.
5/6 = 5 × 7/6 × 7 = 35/42
and
-3/7 = -3 × 6/7 × 6 = -18/42
Therefore, 5/6 + -3/7
= 35/42 + -18/42
= 35 - 18/42
=17/42
(iii) Find the sum:
-9/16 + 5/12
Solution:
LCM of 16 and 12 = (4 × 4 × 3) = 48.
Therefore, -9/16 + 5/12
= 3 × (-9) + 4 × 5/48
= (-27) + 20/48
= -7/48
Step-by-step explanation:
1) Make the denominators same.
eg: 3/4 and 2/5, in this we have find LCM and multiply both numerator and denominator with same number to get same denominator for both fractions. 3/4 × 5/5 = 15/20 and 2/5 × 4/4 = 8/20
2) Now add the numerator
eg: 15/20 + 8/20 = 23/20
3) After that if possible simplify it to the simpilest form.
Hope it helps you