Word Problems Involving Operations with Fractions :
In this section, let us look into some practice problems involving operations with fractions.
Question 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
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)
So 1/8 liter apple juice will get each glass.
Question 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
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)
The required length of each piece of lead is ¾ feet.
Question 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
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.
Question 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
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.
Question 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
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
Hence the required fraction is 91/17.
Question 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
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)
That is, 3 m wood can be cut into 15 equal parts.
After having gone through the stuff given above, we hope that the students would have understood how to solve word problems involving operations with fractions.
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