Word Problems on Fractions: A fraction is a mathematical expression for a portion of a whole. Each portion acquired when we divide the entire whole into parts is referred to as a fraction. When we divide a pizza into parts, for example, each slice represents a fraction of the whole pizza. Fractions are subjected to a variety of operations, including addition, subtraction, multiplication, and division. Fractions are used in many real-life situations.

This article will outline how to construct and solve fraction word problems. Students will come across fraction word problems with answers, fraction problem solving and dividing fractions word problems. It is advisable to practice all the problems thoroughly before attempting the exam. Keep reading to know more about word problems on fractions,, definition, types, solved examples and many more

Definition of Fractions

A fraction is a number that is used to expresses a part per whole. Each part obtained when we divide the whole into several parts is called the fraction.

Example: When we cut an apple into two-part, then each part represents the fraction \(\left(\frac{1}{2}\right)\) of the apple.

A fraction consists mainly of two parts, one is the numerator, and the other one is the denominator. The upper part or topmost part of the fraction is called the numerator, and the bottom part or below part is called the denominator.

Example:

We have mainly three types of fractions: proper fractions, improper fractions, and mixed fractions. They are categorised by the relationship between the numerator and denominator of the fractions.

Word Problems on Fractions

The fraction problem solving consist of a few sentences describing a real-life scenario where a mathematical calculation of fraction formulas are used to solve a problem.

Example: Keerthi took one piece of pizza, which is cut into a total of four pieces. Find the fraction of the pizza taken by Keerthi?

The fraction of pizza taken by Keerthi \(=\frac{1}{4}\)

Some of the word problems on fractions that uses fraction formula are listed below:

1. Word problems on simplification of fractions
2. Word problems on addition and subtraction of fractions
3. Word problems on multiplication of fractions
4. Word problems on dividing fractions
5. Word problems on fractions, percentages, decimals.

Word Problems on Simplifications of Fractions

A fraction in which the numerator and the denominator have no common factor other than “one” is said to be the simplest form of fractions.

Example: Divya took \(8\) apples from the bucket of \(24\) apples. Find the fraction of apples taken by the Divya?
The fraction of apples taken by Divya \(=\frac{8}{24}\) and its simplest form is \(\frac{1}{3}\)

Word Problems on Addition of Fractions

To add the like fractions (Fractions with the same denominators), keep the denominator the same and add the numerator values of the given fractions.

To add the unlike fractions (fractions with different denominators), convert the denominators of the given fractions equal to L.C.M of their denominators. Now add the numerator value and take the denominator of the resultant as L.C.M.

Example: Sahana bought \(\frac{1}{4} \mathrm{~kg}\) of apples and \(\frac{1}{2} \mathrm{~kg}\) of oranges from the shop. Total how many fruits she bought?
The total fruits bought by Sahana \(=\frac{1}{2}+\frac{1}{4}=\frac{1 \times 2+1}{4}=\frac{3}{4} \mathrm{~kg}\)

Word Problems on Subtraction of Fractions

To subtract the like fractions (Fractions with the same denominators), keep the denominator the same and find the difference of the numerator values of the given fractions.

To subtract the unlike fractions (fractions with different denominators), convert the denominators of the given fractions equal to L.C.M of their denominators. Now find the difference of the numerator value and take the denominator of the resultant as L.C.M.

Example: Keerthi travelled \(\frac{2}{5} \mathrm{~km}\) to school. While returning home, she stopped at her friend’s house at a distance of \(\frac{1}{3} \mathrm{~km}\). Find the remaining distance?
The remaining distance needs to be travelled \(=\frac{2}{5}-\frac{1}{3}=\frac{(2 \times 3)-(1 \times 5)}{5 \times 3}=\frac{6-5}{15}=\frac{1}{15} \mathrm{~km}\)

Word Problems on Multiplication of Fractions

To multiply the two or more fractions, find the product of numerators of the given fractions and the product of the denominators of the given fractions separately.

Example: Keerthi had \(Rs.10000\), and she had donated \(\frac{1}{10}\) of the money to the Oldage home. How much amount did she donate?
The amount Keerthi donated \(=\frac{1}{10} \times Rs.10000= Rs. 1000\)

Word Problems on Division of Fractions

The division of fractions is nothing but multiplying the first fraction with the reciprocal of the second fraction. The reciprocal of the fraction is a fraction obtained by interchanging the numerator and denominator.

Example: The area of the rectangle is \(\frac{15}{4} \mathrm{~cm}^{2}\), whose length is \(\frac{5}{2} \mathrm{~cm}\). Find the width of the rectangle?
We know that area of rectangle \(= \text {length} \times \text {bredath}\)
And, breadth \(=\frac{\text { area }}{\text { length }}=\frac{15}{\frac{4}{2}}=\frac{15}{4} \times \frac{2}{5}=\frac{3}{2} \mathrm{~cm}\).

Word Problems on Conversion of Fractions to Percentage

We know that percentages are also fractions with the denominator equals to hundred. To convert the given fraction to a percentage, multiply it with hundred and to convert any percentage value to a fraction, divide with hundred.

Example: Keerthi ate \(\frac{2}{5}\) of the pizza. How much percentage of pizza is eaten by Keerthi?
The percentage of pizza ate by Keerthi \(=\frac{2}{5} \times 100 \%=40 \%\).

Word Problems on Conversion of Fractions to Decimals

Decimal numbers are the numbers (quotient) obtained by dividing the fraction’s numerator with the given fraction’s denominator. To convert the given decimal to the fractional value by writing the given number without decimals and making the denominator equal to \(1\) followed by the zeroes and number of zeroes equal to the number of decimal places.

Example: Keerthi got \(\frac{1}{10}\) of the price of a T.V. as a discount. Find the discount in decimal.
The part of the discount received by a Keerthi as a discount \(=\frac{1}{10}=0.1\)

Solved Examples – Word Problems on Fractions

Q.1. In February \(2021\), a school was working only three-fourths of the total number of days in the month and the remaining number of days given as holidays. How many days did the school work in the month of February?
Ans:
The year \(2021\) is a non-leap year. We know that a non-leap has \(28\) days in February month.
So, the total number of days \(=28\).
Given, the school was working only three-fourths of the total number of days in the month.
The number of days school working in February month \(=\frac{3}{4}\) of \(28\).
\(=\frac{3}{4} \times 28=21\) days
Hence, the school working for \(21\) days in the month of February for the year \(2021\).

Q.2. Keerthi needs \(1 \frac{1}{2}\) cups of sugar for baking a cake. She decided to make \(6\) cakes for her friends. How many cups of sugar did she need for making the \(6\) cakes?
Ans:
Given, Keerthi needs \(1 \frac{1}{2}\) cup of sugar to make a cake.
The total cups of sugar required to make 6 cakes is calculated by multiplying the sugar needed for one cake with the number of cakes that needs to be prepared by Keerthi and is given by \(1 \frac{1}{2} \times 6\)
Convert the above-mixed fraction to an improper fraction by multiplying the denominator with the whole and add to the numerator keeping the same denominator as
\(1 \frac{1}{2}=\frac{(\text { whole×denominator })+\text { numerator })}{\text { denominator }}=\frac{(1 \times 2)+1}{2}=\frac{3}{2}\)
The total cups of sugar needed for making \(6\) cakes \(=\frac{3}{2} \times 6=9\)
Hence, Keerthi needs \(9\) cups of sugar to make \(6\) cakes.

Q.3. An oil container contains \(7 \frac{1}{2}\) litres of oil which are poured into \(2 \frac{1}{2}\) litres bottles. How many bottles are needed to fill \(7 \frac{1}{2}\) litres of oil?
Ans:
Given, a container holds total oil of \(7 \frac{1}{2}\) litres, and the total amount held by each bottle is \(2 \frac{1}{2}\) litres.
Consider the number of bottles required is \(x\).
From the given question, the total oil in the container is equal to the product of oil in each bottle and the number of bottles required.
\(\Rightarrow 7 \frac{1}{2}=x \times 2 \frac{1}{2}\)
\(\Rightarrow \frac{15}{2}=x \times \frac{5}{2}\)
\(\Rightarrow 15=5 x\)
\(\Rightarrow x=\frac{15}{5}=3\)
Therefore, \(3\) bottles are required to fill the total oil in the container.

Q.4. A square garden has the area \(\frac{36}{25} \,\text {sq.ft}\). Find the side of the square garden.
Ans:
Given the area of the square garden is \(\frac{36}{25} \,\text {sq.ft}\).
Let the length of the side of the square garden is \(a\) fts.
We know that area of the square \( = {\rm{side}} \times {\rm{side}} = {a^2}\)
Thus, \(a^{2}=\frac{36}{25}\)
\(\Rightarrow a=\sqrt{\frac{36}{25}}=\frac{\sqrt{36}}{\sqrt{25}}=\frac{6}{5}\) feet.
Hence, the length of the side of the square garden is \(\frac{6}{5}\) feet.

Q.5. At a party, total \(280\) ice-creams are prepared. Four-seventh of them is eaten by the children. Find the ice-creams eaten by the children.
Ans:
Total ice-creams prepared \(=280\)
Number of ice-creams eaten by children \(=\frac{4}{7}\) of \(280=\frac{4}{7} \times 280=160\)
Hence, children ate \(160\) ice-creams.

Summary

In mathematics, a fraction is used to represent a piece of something larger. It depicts the whole’s equal pieces. The numerator and denominator are the two elements of a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The numerator specifies the number of equal parts taken, whereas the denominator specifies the total number of equal parts in the total.

In this article, we have studied the definitions of fractions,  different types of fractions. We also studied the word problems on fractions and their operations. This article gives the word problems on fractions, addition and subtraction of fractions, multiplication of fractions, division of fractions, the simplest form of fractions, conversion of fractions to percentage, decimals etc., with the help of solved examples.

FAQs on Word Problems on Fractions

Here are some of most commonly asked questions on word problems on fractions.

Q.1: How do you solve word problems with fractions?

Ans: To solve word problems with fractions, first, read and write the given data. Write the mathematical form by given data and perform the operations on fractions according to the data.

Q.2: How do you write a fraction division in word problems? 

Ans: The fraction division can be written as keeping the first fraction as it is and multiplying it with the reciprocal of the second fraction.

Q.3: How do you know when to divide or multiply fractions in a word problem?

Ans: To find the product, we need to multiply and to find any one of the quantities, we need to divide.

Q.4: What is an example of a fraction word problem?

Ans: Keerthi ate 40% of the pizza. How much is part of the pizza eaten by Keerthi.

Q.5: What is a fraction?

Ans: A fraction is a number that is used to express a part per whole.

Learn About Conversion Of Fractions

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