Addition  Rational Numbers 

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Operations on Rational numbers
Addition rational numbers :

Steps used for addition rational-numbers :

1) In a rational number, if the denominators are same then just add the numerators.

p / q + r / q = ( p + r ) / q

2) If the denominators are different then first find the LCM of denominators, make the denominators same and then add the numerators.
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Some solved examples on addition rational numbers
Same denominators :

1) 12 / 7 + 23 / 7 = ( 12 + 23 ) / 7 = 35 / 7

As the GCF(HCF) of 35 and 7 is 7 so we can write this rational number in lowest form.

35 / 7 = ( 35 ÷ 7) / ( 7 ÷ 7)

= 5 / 1 = 5
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2) 31 / 3 + 22 / 3 = ( 31 + 22 ) / 3 = 53 / 3

As the GCF(HCF) of 53 and 3 is 1 so 53 / 3 is the lowest form.
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Different denominators :

3) 5 / 12 + 3 / 8

Solution :

5/ 12 + 3 / 8 , here the denominators are different so we have to find the LCM of 12 and 8. LCM of 12 and 8 = 24

5 / 12 = ( 5 x 2 ) / ( 12 x 2) = 10 / 24

3 / 8 = ( 3 x 3 ) / ( 8 x 3) = 9 / 24

Now the denominators are same so add the numerators.

( 10 + 9 ) / 24 = 19 / 24
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4) 7 / 9 + 4

Solution :

7 / 9 + 4 / 1 ( since 4 = 4 /1 )

Here the denominators are different . LCM of 9 and 1 = 9

7 / 9 = ( 7 x 1) / ( 9 x 1) = 7 / 9

4 / 1 = ( 4 x 9) / ( 1 x 9) = 36 / 9

Now the denominators are same so add the numerators.

( 7 + 36 ) / 9 = 43 / 9
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5) Add 3 / 8 and – 5 / 12

Solution :

3/ 8 + (- 5 ) / 12 , here the denominators are different so we have to find the LCM of 12 and 8. LCM of 12 and 8 = 24

3 / 8 = ( 3 x 3 ) / ( 12 x 2) = 9 / 24

- 5/ 12 = ( -5 x 2 ) / ( 8 x 3) = - 10 / 24

Now the denominators are same so add the numerators.

[ ( 9 + ( - 10 )] / 24 = - 1 / 24
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Rational number

Representation of rational number on number line
Comparison of rational number
Addition rational numbers
Subtraction of rational numbers
Conversion of rational numbers to decimal
Irrational Numbers

Number system Page

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