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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