WORD PROBLEMS ON FRACTIONS

Problem 1 :

A cookie factory uses 1/4 of a barrel of oatmeal in each batch of cookies. The factory used 1/2 of a barrel of oatmeal yesterday. How many batches of cookies did the factory make ?

Solution :

Amount of oatmeal used in each batch of cookies is

=  1/4 of a barrel

No. of cookies made yesterday is

=  Oatmeal used yesterday / Oatmeal used in each batch 

=  (1/2) / (1/4)

=  1/2 ⋅ 4/1

=  2

So, the factory made 2 batches of cookies yesterday. 

Problem 2 :

Of the students in the band, 1/4 play the flute and another 1/10 play the clarinet. What fraction of the students in the band play either the flute or the clarinet ?

Solution :

Fraction of the students in the band play either the flute or the clarinet is 

=  1/4 + 1/10

LCM of (4, 10) is 20. 

So, make each denominator as 20 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 2. 

Then we have, 

=  (1 ⋅ 5) / (4 ⋅ 5)  +  (1 ⋅ 2) / (10 ⋅ 2)

=  5/20 + 2/20

=  (5 + 2) / 20

=  7 / 20

So, the fraction of the students who play either the flute or the clarinet is 7/20.

Problem 3 :

Lily rode her bicycle 5/4 miles from her house to the park. Then she rode 3/2 miles from the park to the library. How many miles did Lily ride in all ?

Solution :

Total number of miles that Lily rode in all is 

=  5/4 + 3/2

LCM of (4, 2) is 4. 

So, make each denominator as 4 by multiplying the numerator and denominator of the first fraction by 1 and the second fraction by 2. 

Then we have, 

=  (5 ⋅ 1) / (4 ⋅ 1)  +  (3 ⋅ 2) / (2 ⋅ 2)

=  5/4 + 6/4

=  (5 + 6) / 20

=  11 / 4

=  2¾

So, Lily rode 2¾ miles in all. 

Problem 4 :

At the dealership where Mary works, she fulfilled 1/6 of her quarterly sales goal in January and another 3/10 of her sales goal in February. If her quarterly sales goal is $12,000, what amount of sales did she make in January and February ?

Solution :

Fraction of her sales done in January and February is

=  1/6 + 3/10

LCM of (6, 10) is 30. 

So, make each denominator as 30 by multiplying the numerator and denominator of the first fraction by 5 and the second fraction by 3. 

Then we have, 

=  (1 ⋅ 5) / (6 ⋅ 5)  +  (3 ⋅ 3) / (10 ⋅ 3)

=  5/30 + 9/30

=  (5 + 9) / 30

=  14 / 30

=  7/15

Amount of sales she made in January and February is

=  7/15 of quarterly sales goal 

=  7/15 ⋅ 12000

=  5600

So, amount of sales Mary made in January and February is $5,600. 

Problem 5 :

Lucy made strawberry jam and raspberry jam. She made enough strawberry jam to fill 5/6 of a jar. If she made 2 times as much raspberry jam as strawberry jam, how many jars would the raspberry jam fill ?

Solution :

Amount of strawberry jam made by Lucy is 

=  5/6 of a jar

2 times as much raspberry jam as strawberry jam is 

=  2 ⋅ 5/6 of a jar

=  5/3 of a jar

=  1 ⅔ of a jar

So, Lucy would make enough raspberry jam to fill 1 ⅔ jars.

Problem 6 :

David's salary is $1800. David spent 2/3 of the total money for food. He spent 1/2 of the remaining for his kids education and saved the rest. How much did he save ? 

Solution :

Money spent on food  is

=  1800 ⋅ 2/3 = 1200

Remaining  =  1800 - 1200  =  600 -------(1)

Money spent on kids education is

=  1/2 of remaining

=  1/2 ⋅ 600

=  300 --------(2)

Then, his savings is

=  (1) - (2)

=  600 - 300

=  300

So, his savings is $300. 

Problem 7 :

A, B and C are friends. A has 1/3 of money that B has. C has 1/2 of money that A has. If they all together have  $450. How much money do A, B and C have separately ? 

Solution :

Let us assume that B has the money "x". 

Then, A  =  (1/3)x  =  x/3    

C  =  1/2 of A 

C  =  1/2 ⋅ x/3

C  =  x/6

Given : A + B + C  =  300 -------> x/3 + x + x/6  =  450

4x/12 + 12x/12 + 2x/12  =  450

(4x+12x+2x)/12  =  450

18x/12  =  450

x  =  300 

So, we have

A  =  x/3  =  300/3  =  100

B  =  x  =  300

C  =  x/6  =  300/6  =  50

So, A has $100, B has $450 and C has $50. 

Problem 8 :

John's present age is 1/3 of David's age  5 years back.If David is 20 years old now, find the present age  of John.  

Solution :

Present age of David  =  20 years

David's age 5 years back  =  20 - 5  =  15 years

John's present age is 1/3 of David's age  5 years back

John's present age is

=  1/3 of 15 years

=  (1/3) ⋅ 15

=  5 years. 

So, John's present age is 5 years. 

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