Fractions are part of mathematics; in fact, they are more of a strong foundation for those who are into classes 4 to 8 CBSE, where they lay out the foundation of advanced math. This guide helps you understand the basics of fractions and their types of operations and provides you with all the tips to ace the topic whether you are going to sit in the exam or brushing up. This blog will simplify fractions and be fun to learn.
What Are Fractions?
A fraction is a part of a whole. It is written in the form of a/b, where:
a (numerator): Shows the number of parts taken.
b (denominator): Represents the total number of equal parts of the whole.
For instance, if a pizza is divided into 8 slices, and you eat 3, then the fraction of pizza you ate is ⅜.
Types of Fractions:
Once the types of fractions are known, problems can be easily solved and include:
- Proper Fractions: The denominator is larger than the numerator. For example, ⅗.
- Improper Fractions: The numerator is bigger, or equal, to the denominator. For example, 7/4.
- Mixed Fractions: A whole and a proper fraction together. For example, 2 ⅓
- Like Fractions: They share the same denominator. For example, 2/7 and 5/7
- Unlike Fractions: Have different denominators. For instance, ¾, ⅝.
- Equivalent Fractions: Fractions with the same value are ½ is equivalent to 2/4.
Operations on Fractions
Operations on fractions is one of the most important skills for CBSE students.
1. Addition and Subtraction:
- For Like Fractions: Add or subtract the numerators, keeping the denominator unchanged. Example: 2/7 + 3/7 = 5/7
- For Unlike Fractions: Find the Least Common Denominator (LCM), convert the fractions to like fractions, and then add or subtract.
Example: ¼ + ⅔ → 3/12 + 8/12 = 11/12
2. Multiplication:
Multiply the numerators and denominators directly.
Example: ⅖ × ¾ = 6/20 = 3/10.
3. Division:
Change the sign of the second fraction (reciprocal) and multiply.
Example: ¾ ÷ ⅖ = ¾ × 5/2 = 15/8.
Converting Mixed Fractions to Improper Fractions
To change a mixed fraction (such as 2 ⅓) to an improper fraction:
Multiply the number (integer) by the denominator and add the numerator.
Keep the denominator as is.
Example:
2 ⅓ = 2 × 3+ 1÷ 3 = 7/3
Reducing or Simplifying Fractions
To reduce a fraction, divide the numerator and denominator by their greatest common divisor (GCD).
Example:
12/16 = 12 ÷ 4 / 16 ÷ 4 = ¾
Fractions in Real Life
Fractions aren’t bookworms. They are found in:
- Cooking: Measuring sugar 1/2 cup or more.
- Money: Splitting a bill with a friend, etc.
- Time: Half-hour or quarter hour
- Sports: Cricket batting averages.
Tips for Conquering Fractions
- Do LCM and GCD calculations. Those form the basic framework for manipulating fractions.
- Visualize using a pie chart or a number line.
- Solve word problems that enhance your capacity to use fractions in practical situations.
- Practice different types of problems daily to gain confidence.
Common Mistakes to Avoid
- Remember, only numerators are added or subtracted.
- Always simplify your answers for better clarity and marks.
- Always flip the second fraction while dividing.
Why Fractions Matter in CBSE Exams
Fractions come up in almost every topic, from arithmetic to algebra. Doing well in fractions can help improve your overall performance in math. The concept can be applied in solving application-based and higher-order thinking (HOT) questions that are included in the CBSE exams.
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