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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.
Definition of FractionsA 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 FractionsThe 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? Some of the word problems on fractions that uses fraction formula are listed below:
Word Problems on Simplifications of FractionsA 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? Word Problems on Addition of FractionsTo 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? Word Problems on Subtraction of FractionsTo 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? Word Problems on Multiplication of FractionsTo 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? Word Problems on Division of FractionsThe 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? Word Problems on Conversion of Fractions to PercentageWe 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? Word Problems on Conversion of Fractions to DecimalsDecimal 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. Solved Examples – Word Problems on FractionsQ.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? 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? 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? Q.4. A square garden has the area \(\frac{36}{25} \,\text {sq.ft}\). Find the side of the square garden. 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. SummaryIn 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 FractionsHere 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 We hope this detailed article on Word Problem on Fractions helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest. Stay tuned to Embibe to learn more important concepts What is an example of a fraction word problem?Example 1: Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether? Analysis: To solve this problem, we will add two fractions with like denominators. Answer: Rachel rode her bike for three-fifths of a mile altogether.
What are the 3 simple steps to multiply fractions?Step 1: Multiply the numerators. Step 2: Multiply the denominators. Step 3: Reduce the resultant fraction to its lowest terms.
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