Fractions Made Fun: A Class 5 Guide to Mastering Parts of a Whole
Published by Ganit Charcha
| Category - Middle School Math Topics | 2025-07-22 02:16:05
What is a Fraction? In mathematics, a fraction represents a part of a whole or a ratio between quantities. It shows how many equal parts are taken from a total and is a fundamental concept for comparing and measuring portions.
Components of a Fraction A fraction is made up of two key parts: Numerator: The number above the fraction bar, indicating how many parts are being considered. Denominator: The number below the fraction bar, showing how many equal parts the whole has been divided into. These two numbers are separated by a horizontal line, known as the fraction bar.
Example Imagine a pineapple sliced into 8 equal pieces. If you eat 3 of them, this can be represented by the fraction $\frac{3}{8}$. Here, 3 (the numerator) tells us how many slices were eaten, and 8 (the denominator) indicates the total number of slices.
Fractions in Everyday Life Fractions are not just mathematical concepts—they appear in many real-world scenarios: Eating Chocolate or Candy Bars: Imagine a chocolate bar divided into 10 equal squares. If you eat 4 squares, you’ve eaten $\frac{4}{10}$ of the chocolate. The remaining $\frac{6}{10}$ is still left. Playing Games: In a board game, if a turn lasts for 1 minute and you have already played for 30 seconds, you’ve completed $\frac{1}{2}$ of your turn. Classroom Activities: If there are 20 students in your class and 5 are wearing red shirts, then $\frac{5}{20}$ or $\frac{1}{4}$ of the class is wearing red. Using a Ruler: A ruler is often marked in halves $\frac{1}{2}$, quarters $\frac{1}{4}$, and eighths $\frac{1}{8}$. So if you measure something and it’s $\frac{3}{4}$ of an inch long, you’re using a fraction. Watching a Movie: If a movie is 2 hours long and you’ve watched 1 hour, you’ve watched $\frac{1}{2}$ the movie. If you’ve watched 30 minutes, that’s $\frac{1}{4}$ of the movie. Sports and Scores: In a basketball game, if a team scores 18 points out of a total possible 36, they have scored $\frac{18}{36}$ or $\frac{1}{2}$ of the maximum points. Folding Paper for Crafts: When you fold a paper in half to make a card or in quarters to create a fan, you are dividing it into $\frac{1}{2}$, $\frac{1}{4}$, etc. Music and Rhythms: In music, notes often represent fractions of a beat. A half note is $\frac{1}{2}$, a quarter note is $\frac{1}{4}$, and so on. Reading Books: If a book has 100 pages and you’ve read 75, then you’ve read $\frac{3}{4}$ of the book. Cooking and Baking: Recipes often use fractional measurements like $\frac{1}{2}$ cup of sugar or $\frac{3}{4}$ teaspoon of vanilla essence. Measurement and Construction: Whether measuring fabric or cutting wood, fractions help achieve precise lengths like $\frac{3}{4}$ inch or $\frac{5}{8}$ metre. Time: Expressions such as “half past” or “quarter to” refer to fractions of an hour. Shopping and Discounts: Sales often use percentages, which are forms of fractions—like 25% off, which means one-fourth of the price is reduced. Sharing and Dividing: Splitting food, bills, or tasks evenly among people naturally involves understanding fractions. A strong grasp of fractions lays the foundation for deeper mathematical learning and helps us navigate numerous real-life activities with accuracy and confidence.
Types of Fractions
Proper Fractions: The numerator is smaller than the denominator. Example: $\frac{3}{5}$, $\frac{2}{7}$ These represent values less than 1. Improper Fractions: The numerator is greater than or equal to the denominator. Example: $\frac{7}{4}$, $\frac{9}{9}$ These represent values equal to or greater than 1.
Mixed Numbers: A combination of a whole number and a proper fraction. Example: $2\frac{1}{3}$ means $2 + \frac{1}{3} = \frac{7}{3}.$
Like and Unlike Fractions: Like fractions have the same denominator, e.g., $\frac{2}{7}$ and $\frac{5}{7}.$ Unlike fractions have different denominators, e.g., $\frac{1}{3}$ and $\frac{2}{5}.$
Equivalent Fractions: Two or more fractions that represent the same part of a whole. For example, $\frac{1}{2} = \frac{2}{4}$. This can be visualized as follows. A cake is being divided into two equal halves and you get one of the half. This is exactly equivalent to the cake being divided into 4 equal halves and you got 2 of the pieces. In either case, the emount cake that you received is one half of the whole cake. Same multiple of both numerator and denominator can generate infinite number of equivalent fractions of a given fraction. $\frac{1}{2} = \frac{1 . 2} {2 . 2} = \frac{2}{4}$ $= \frac{1 . 3} {2 . 3} = \frac{3}{6}$ $= \frac{1 . 4} {2 . 4} = \frac{4}{8}$ $= \frac{1 . 5} {2 . 5} = \frac{5}{10}$ Therefore, $\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}$ are all fractions which are equivalent to $\frac{1}{2}$.
Simplest Form (or Lowest Terms): A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. Note that, finding the Simplest form of a fraction is also finding an exact equivalent fraction where instead of multiplying both numerator and denominator, we divide both numerator and denominator by the HCF of numerator and denominator. Example: $\frac{8}{12}$ = (8 ÷ 4)/(12÷4) =$\frac{2}{3}$ after dividing both by 4, where HCF of 8, 12 is equal to 4. Therefore, a fraction is said to be in lowest form when the numerator and denominator will be coprime to each other, or in other words HCF of numerator and denominator is 1.
Operations on Fractions
Addition and Subtraction: When denominators are the same, simply add or subtract numerators. Example: $\frac{3}{8} + \frac{2}{8} = \frac{3 + 2}{8} = \frac{5}{8}$ When denominators are different, find the LCM (Least Common Multiple), convert both fractions to equivalent fractions with the same denominator, and then add/subtract. Example: $\frac{1}{4} + \frac{2}{3}$ LCM of 4 and 3 is 12 $\frac{1}{4} = \frac{3}{12}$, $\frac{2}{3} = \frac{8}{12}$ Therefore, $\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}$
Multiplication: Multiply numerators together and denominators together. Example: $\frac{2}{3} . \frac{4}{5} = \frac{2.4}{3.5} = \frac{8}{15}$
Reciprocal of a Fraction: The reciprocal of a fraction is obtained byfliping the numerator and the denominator. For example: 1. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. 2. The reciprocal of $\frac{5}{1}$ (which is just $5$) is $\frac{1}{5}$. 3. Similarly, the reciprocal of $\frac{1}{7}$ is $\frac{7}{1}$ which is $7$. Key Points: 1. If the fraction is $\frac{a}{b}$, its reciprocal is $\frac{b}{a}$. 2. The reciprocal of a number multiplied by the number itself equals 1: $$\frac{a}{b} \times \frac{b}{a} = 1$$ 3. Zero does not have a reciprocal, as division by 0 is undefined.
Division: Flip the second fraction (i.e., take the reciprocal of the divisor fraction) and multiply. After multiplication, simplify the result into the lowest form. Example: $\frac{2}{3} ÷ \frac{4}{5} = \frac{2}{3} . \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$
Converting Mixed Numbers to Improper Fractions: Multiply the whole number by the denominator, add the numerator, and write the result over the denominator. Example: $2\frac{3}{5} = \frac{(2.5) + 3}{5} = \frac{13}{5}$
Converting Improper Fractions to Mixed Numbers: Divide numerator by denominator. The quotient is the whole number and the remainder is the new numerator. Example: $\frac{17}{4} = 4\frac{1}{4}$
Practice Problems (with Solutions)
Let us now move to more advanced problems typically seen in mathematics examinations for classes V and VI. Problem 1: A jar is $\frac{2}{3}$ full of milk. If $3$ litres of milk is removed, it becomes $\frac{1}{3}$ full. What is the total capacity of the jar?
Solution The amount milk that was removed = $\frac{2}{3} - \frac{1}{3} = \frac{1}{3}$ of the total capacity of the jar. We know that $3$ litres of milk has been removed, which is $\frac{1}{3}$ of the total capacity of the jar. Therefore, ($\frac{1}{3}$) x Total capacity of jar = $3$ litre ==> Total capacity of the jar = $9$ litres. Answer: $9$ litres
Problem 2: A cake was cut into $12$ equal pieces. Rina ate $\frac{1}{4}$ of the cake, and John ate $\frac{1}{3}$ of it. How many pieces are left?
Solution Total pieces = $12$ Rina ate $\frac{1}{4}$ of $12$ = $3$ pieces John ate $\frac{1}{3}$ of $12$ = $4$ pieces Total eaten = $3 + 4 = 7$ pieces Remaining = $12 − 7 = 5$ pieces Answer: $5$ pieces
Problem 3: Which is greater: $\frac{7}{12}$ or $\frac{5}{8}$?
Solution LCM of $12$ and $8$ is $24$ $\frac{7}{12} = \frac{14}{24}$ $\frac{5}{8} = \frac{15}{24}$ Since $15$ > $14$, so $\frac{5}{8}$ is greater Answer: $\frac{5}{8}$
Problem 4: A basket contains red, blue, and green balls. $\frac{3}{10}$ are red, $\frac{2}{5}$ are blue, and the rest are green. What fraction of balls are green?
Solution Fraction of Red balls = $\frac{3}{10}$, Fraction of Blue balls = $\frac{2}{5}$ = $\frac{3}{10}$ Fraction of Red and Blue balls together = $\frac{3}{10} + \frac{3}{10} = \frac{7}{10}$ Therefore, Fraction of Green balls = $1 − \frac{7}{10} = \frac{3}{10}$ Answer: $\frac{3}{10}$
Problem 5: What fraction should be added to $\frac{5}{9}$ to make it $1$?
Solution The fraction that is requiredto be added = $1 − \frac{5}{9} = \frac{4}{9}$ Answer: $\frac{4}{9}$
Problem 6: If $\frac{3}{5}$ of a number is $24$, what is the number?
Solution Given, $\frac{3}{5}$ of a Number = $24$ ==> $\frac{3}{5}$ x Number = $24$ ==> Number = $\frac{24 . 5}{3} = 40$ Answer: $40$
Problem 7: A tank is 2/5 full. After adding 600 litres of water, it becomes 4/5 full. Find the capacity of the tank. Solution The amount of water added = $600$ litres. Therefore, the fraction of the tank which got filled by this $600$ litres = $\frac{4}{5} - \frac{2}{5} = \frac{2}{5}$ $\frac{2}{5}$ of Capacity of the Tank = $600$ litres ==> Capacity of the Tank = $\frac{600 . 5}{2} = 1500$ litres Answer: $1500$ litres
Problem 8: What is the sum of $\frac{3}{7}$, $\frac{5}{14}$ and $\frac{2}{21}$?
Problem 9: A ribbon is $\frac{7}{8}$ metres long. How much should be cut off to leave $\frac{1}{4}$ metre? Solution The amount of ribbon to be cut off = $\frac{7}{8} − \frac{1}{4} = \frac{7 − 2}{8} = \frac{5}{8}$ Answer: $\frac{5}{8}$ metres
Problem 10: If A does $\frac{2}{5}$ of a task, and B does $\frac{1}{3}$ of it, what fraction of the task remains?
Solution Total work done by A and B = $\frac{2}{5} + \frac{1}{3}= \frac{6 + 5}{15} = \frac{11}{15}$ Remaining work = $1 − \frac{11}{15} = \frac{4}{15}$ Answer: $\frac{4}{15}$
