WORD PROBLEMS WITH RATIONAL NUMBERS

Problem 1 :

In a recipe making, every 1  1/2 cup of rice requires 2  3/4 cups of water. Express this, in the ratio of rice to water.

Solution :

Quantity of rice  =  1  1/2  =  3/2

Quantity of water required  =  2  3/4  =  11/4

Ratio between rice and water  =  (3/2) : (11/4)

=  (3/2) x (4/11)

=  6/11

=  6 : 11

Problem 2 :

Ravi multiplied 25/8 and 16/15 to obtain 400/120. He says that the simplest form of this product is 10 3 and  Chandru says the answer in the simplest form is 3 1/3. Who is correct? (or) Are they both correct? Explain.

Solution :

By multiplying the fractions 25/8 and 16/15, we get 400/120

By simplifying this, we get

=  40/12  =  10/3 (improper fraction)

By changing this improper fraction into mixed form, we will get

=  3  1/3

So, both are correct.

Problem 3 :

A piece of wire is 4/5 m long. If it is cut into 8 pieces of equal length, how long will each piece be?

Solution :

Original length of wire  =  4/5

Number of pieces to be cut out  =  8

length of each piece  =  (4/5)  ÷ 8

=  (4/5)  (1/8)

=  1/10 m

Length of each part is 1/10 m.

Problem 4 :

Find the length of a room whose area is 153/10 sq.m and whose breadth is 2  11/20 m.

Solution :

Area of room  =  153/10

Breadth  =  2  11/20  =  51/20

length  =  ?

Length x breadth  =  (153/10) ÷ (51/20)

=  (153/10) x (20/51)

=  3(2)

=  6

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