**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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