ADD AND SUBTRACT RATIONAL NUMBERS WORD PROBLEMS

Problem 1 :

The sum of two rational numbers is 17/4 . If one of the numbers is 5/2 , find the other number.

Solution :

The sum of two rational numbers  =  17/4 

One of the numbers  =  5/2

Let "x" be the other rational number

x + (5/2)  =  17/4

In order to solve for "x", we have to subtract 5/2 on both sides

x + (5/2) - (5/2)  =  (17/4) - (5/2)

x  =  (17/4) - (5/2)

Since the denominators of these two fractions are not same, we have to take L.C.M

L.C.M (4, 2) = 4

  =  (17/4) - (5/2) x (2/2) 

  =  (17/4) - (10/4)

  =  (17 - 10)/4

  =  7/4

So, the required other number is 7/4.

Problem 2 :

What number should be added to 5/6 so as to get 49/30.

Solution :

Let "x" be the required number

x + (5/6) = 49/30

In order to solve for "x", we have to subtract 5/6 on both sides

x + (5/6) - (5/6) = (49/30) - (5/6)

Since the denominators of these two fractions are not same, we have to take L.C.M

L.C.M (30, 6)  =  30

x  =  (49/30) - (5/6) x (5/5)

x = (49/30) - (25/30)

=  (49 - 25)/30

=  24/30

=  4/5

So, the required number is 4/5.

Problem 3 :

A shop keeper sold 7  3/4 kg, 2  1/2 kg and 3  3/5 kg of sugar to three customers in a day.Find the total weight of sugar on that day?

Solution :

To find the total weight of sugar on that day, we have to add the above quantities.

Total weight of sugar  =  7  3/4 + 2  1/2 + 3  3/5

Converting the above mixed fractions as improper fractions, we get 

  =  (31/4) + (5/2) + (18/5)

Since the denominators of these two fractions are not same, we have to take L.C.M

L.C.M (4, 2, 5)  =  20

  =  (31/4) x (5/5) + (5/2) x (10/10) + (18/5) x (4/4)

  =  (155/20) + (50/20) + (72/20)

  =  (155 + 50 + 72)/20

  =  277/20

=  13  17/20

So, the total weight of sugar sold is 13  17/20 kg.

Problem 4 :

John bought 25 kg of Rice and he used 1 3/4 kg on the first day, 4 1/2 kg on the second day. Find the remaining quantity of rice left.

Solution :

Rice used on first day  =  1  3/4 kg

Rice used on second day  =  4  1/2 kg

Quantity of rice used on first and second day

=  (1  3/4) + (4  1/2)

Converting the above mixed fraction in to improper fraction, we get 

  =  7/4 + 9/2

=  7/4 + (9/2) x (2/2)

= 7/4 + 18/4

=  (7 + 18)/4

=  25/4

Remaining quantity of rice left  =   25 -  (25/4)

=  (100 - 25)/4 

=  75/4

=  18  3/4 kg 

Remaining quantity of rice is 18  3/4 kg.

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