ADD AND SUBTRACT RATIONAL NUMBERS WORKSHEET

Problem 1 :

Problem 2 :

Problem 3 :

Problem 4 :

Problem 5 :

Problem 6 :

Detailed Answer Key

Problem 1 :

Simplify the following and write your answer as a proper fraction or as a whole or mixed number.

Solution :

Since the denominators are same, we can put only one common denominator and combine the numerators.

  =  (3 + 4)/7 

  =  7/7

  =  1

Problem 2 :

Simplify the following and write your answer as a proper fraction or as a whole or mixed number.

Solution :

Since the denominators are same, we can put only one common denominator and combine the numerators.

  =  (12 - 4)/13 

  =  8/13

Problem 3 :

Simplify the following and write your answer as a proper fraction or as a whole or mixed number.

Solution :

Since the denominators are not same, we need to take L.C.M in order to convert the denominators same.

L.C.M (4, 3) = 12

  =  (3/4) x (3/3) + (2/3) x (4/4)

  =  (9/12) + (8/12) 

  =  (9 + 8)/12

  =  17/12

The numerator is grater than the denominator, we have to convert it into mixed fraction. 

=  1 5/12

Problem 4 :

Simplify the following and write your answer as a proper fraction or as a whole or mixed number.

Solution :

Since the denominators are not same, we need to take L.C.M in order to convert the denominators same.

L.C.M (3, 4) = 12

  =  (2/3) x (4/4) - (1/4) x (3/3)

  =  (8/12) - (3/12) 

  =  (8 - 3)/12

  =  5/12

Problem 5 :

Simplify the following and write your answer as a proper fraction or as a whole or mixed number.

Solution :

Now we need to consider the given question as two parts.

First we have to simplify the fractions inside the parenthesis.

Subtract 2/9 from the simplified answer.

  =  {(8/9) - (1/9)} - (2/9)

  =  (8- 1)/9 - (2/9) 

  =  (7/9) - (2/9)

  =  (7 - 2)/9

=  5/9

Problem 6 :

Simplify the following and write your answer as a proper fraction or as a whole or mixed number.

Solution :

Since the denominators are not same, we have to L.C.M in order to convert the denominators same.

L.C.M (4, 5, 8) = 40

  = (3/4) x (10/10) + (2/5) x (8/8) + (4/8) x (5/5) 

  =  (30 + 16 + 20)/40

  =  66/20

  =  33/10

Since the numerator is greater than the denominator, we have to convert into mixed fraction.

=  3 3/10

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