WORD PROBLEMS INVOLVING OPERATIONS WITH FRACTIONS

Problem 1 :

Mary poured 5/8 liter of apple juice equally in to 5 glasses. How much of apple juice was there in each glass?

(A) 1/8 liter      (B)  1/5 liter    (C) 1/6 liter

Solution :

Original quantity of apple juice  =  5/8 liter

Number of glasses to be divide  =  5

Quantity of apple juice in each glass  =  (5/8) ÷ 5

Here we can consider 5 as 5/1

=   (5/8) ÷ (5/1)

=  (5/8)  (1/5)

=  1/8

So 1/8 liter apple juice will get each glass.

Problem 2 :

John cuts lead strips to make stained-glass windows. He has a 3 ¾ foot strip of lead and cuts into 5 equal pieces. How long is each piece of lead?

(A) 1/6 feet       (B)  3/4 feet     (C) 2/3 feet

Solution :

Original length of the lead strip  =  3  ¾ foot

Length of each lead strip  =  3 ¾ foot ÷ 5  

  =  15/4 ÷ 5  

  =  (15/4)  (1/5)

  =  3/4

The required length of each piece of lead is ¾ feet.

Problem 3 :

Mrs.Mathew divided ¾ kg of grapes equally among 6 children. How many kilograms of grapes did each child get?

(A) 1/8 kg        (B)  3/11 kg           (C) 2/3 kg

Solution :

Quantity of grapes that Mrs.Mathew had  =  3/4 kg

Number of children is be divided = 6

Quantity of grapes that each children will get 

  =  (original quantity of grapes)/(Number of children)

  =  (3/4) ÷ 6

  =  (3/4)  (1/6)

  =  1/8 kg

That is each child will get 1/8 kg of grapes.

Problem 4 :

The perimeter of square piece of paper is  3/4 m. What is the length of its side?

(A) 1/15 m      (B)  3/16 m   (C) 2/3 m

Solution :

Perimeter of square piece  =  3/4 m

Perimeter of any square  =  4a

4a  =  3/4 m

The length of four sides  =  3/4 m

length of one side  =  (3/4)  ÷ 4

= (3/4)  (1/4)

The length of each side of a square is 3/16 m.

Problem 5 :

The product of two fractions is 30 1/3. One of them is 5 2/3.  Find the other?

(A) 91/17      (B)  15/19      (C) 25/97

Solution :

Let x be the required fraction.

One of the fraction  =  5   2/3  =  17/3

Product of two fractions  =  30  1/3  =  91/3

(17/3) ⋅ x  =  91/3

x  =  91/3 ÷ (17/3)

x  =  (91/3) ⋅ (3/17)

x  =  91/17

So, the required fraction is 91/17.

Problem 6 :

How many pieces of wood each 1/5 m long can be cut from a piece 3 m long ? 

(A) 18  pieces     (B)  11 pieces     (C)  15 pieces

Solution :

Length of the given wood  =  3 m 

Length of each piece  =  (1/5) m

Length of each pieces which has been cut  

  =  Length of wood/(measurement of wood piece)

=  3 / (1/5)

=  15

That is, 3 m wood can be cut into 15 equal parts.

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