**Word Problems on Fractions :**

In this section, we are going to learn, how to solve word problems on fractions step by step.

Let us look at some examples on "Word problems on fractions".

**Example 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

Hence, the factory made 2 batches of cookies yesterday.

**Example 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

L.C.M 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

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

**Example 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

L.C.M 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

Hence, Lily rode 2¾ miles in all.

**Example 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

L.C.M 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

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

**Example 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

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

**Example 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

Hence, his savings is $300.

**Example 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

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

**Example 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.

Hence, John's present age is 5 years.

After having gone through the stuff given above, we hope that the students would have understood "Word problems on fractions".

Apart from the stuff given above, if you would like to know more about "Word problems on fractions", please click here

Apart from the stuff "Word problems on fractions", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...