Q. 5 Solve the following problems:

1. Naina was given 1 1/2 piece of cake and Najma was given 1 1/3 piece of cake. Find the total amount of cake given to both of them.

Answer: Here we have to add two fractions 1 1/2 and 1 1/3 and we get the answer.

First convert mixed fraction to improper fraction:

1 1/2 = (1 x 2 + 1) / 2 = 3 /2

 1 1/3 = ( 1 x3 + 1) / 3 = 4 /3

Now convert improper fraction to like fraction using LCM

Here LCM is 6 so we get

3 x 3 / 2 x 3 = 9/6

4 x 2 / 3 x 2 = 8/6

Adding the above two fraction is straightforward:

9/6 + 8/6 = (9 + 8) / 6 = 17/6

Thus the answer is 17/6

2. Aakash bought vegetables weighing 10 kg. Out of this 3 kg 500 gm is onions, 2 kg 75 gms are tomatoes and the rest is potatoes. What is the weight of potatoes?

Answer: Total weight of vegetables = 10 kg = weight of onions + weight of potatoes + weight of tomatoes

Thus weight of potatoes = 10 kg - weight of onions - weight of tomatoes

Now first find weight of onions = 3 kg 500 gm which when converted in kg gives 3 + 500/1000 = 3.5 kg

Weight of tomatoes = 2 kg 75 gms which when converted in kg gives 2 + 75/1000 = 2.075 kg

Thus weight of potatoes = 10 - 3.5 - 2.075 = 4.425 kg which is 4 kg and 425 gms.