Fractions
Overview
A fraction represents a part of a whole. When we divide a whole into equal parts and take some of those parts, we get a fraction. Fractions are written as a/b where 'a' is the numerator (parts taken) and 'b' is the denominator (total equal parts). Fractions are used in everyday life — cutting a pizza, measuring ingredients, or sharing things equally. This chapter covers types of fractions, comparing them, and basic operations like addition and subtraction.
Typed Notes
Types of Fractions
Fractions come in three main types. A proper fraction has a numerator smaller than its denominator, like 2/5 or 3/8 — its value is always less than 1. An improper fraction has a numerator equal to or greater than the denominator, like 5/3 or 7/7 — its value is 1 or more. A mixed number is a whole number combined with a proper fraction, like 1 and 2/3. We can convert between improper fractions and mixed numbers easily by dividing or multiplying.
Equivalent Fractions and Simplest Form
Equivalent fractions look different but have the same value. We make them by multiplying or dividing both numerator and denominator by the same number. For example, 1/2 = 2/4 = 4/8. A fraction is in its simplest form when the numerator and denominator share no common factor other than 1. To simplify, divide both by their Highest Common Factor (HCF). For example, 6/8 — HCF of 6 and 8 is 2, so 6/8 = 3/4, which is the simplest form.
Comparing Fractions
To compare fractions with the same denominator, simply compare numerators — the bigger numerator means the bigger fraction. For example, 3/7 is greater than 2/7. To compare fractions with different denominators, first convert them to equivalent fractions with the same denominator (called the Least Common Denominator or LCD). For example, to compare 1/2 and 1/3, convert to 3/6 and 2/6. Since 3/6 is greater than 2/6, we know 1/2 is greater than 1/3.
Addition and Subtraction of Fractions
When fractions have the same denominator, add or subtract only the numerators and keep the denominator the same. For example, 2/7 + 3/7 = 5/7. When denominators are different, first find the LCM of the denominators to get a common denominator, convert each fraction, then add or subtract. For example, 1/2 + 1/3: LCM of 2 and 3 is 6, so 3/6 + 2/6 = 5/6. Always simplify your answer if possible.
Key Concepts
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- 01A fraction a/b means 'a parts out of b equal parts'; numerator is on top, denominator is on bottom.
- 02Proper fractions have numerator less than denominator (e.g., 3/5); improper fractions have numerator greater than or equal to denominator (e.g., 7/4).
- 03A mixed number combines a whole number and a proper fraction, e.g., 2 and 1/3, and can be converted to an improper fraction.
- 04Equivalent fractions are different fractions that represent the same value, e.g., 1/2 = 2/4 = 3/6.
- 05To compare, add, or subtract fractions, we need a common denominator (same bottom number).
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Convert the mixed number 3 and 2/5 into an improper fraction.
Simplify the fraction 12/18 to its simplest form.
Add the fractions 2/5 and 1/3.
Which fraction is greater: 3/4 or 5/7?
Subtract 1/4 from 3/4.
Fractions represent equal parts of a whole, written as numerator over denominator. They can be proper, improper, or mixed numbers. Equivalent fractions show the same value in different forms, and simplifying uses the HCF. Comparing fractions needs a common denominator. Adding and subtracting fractions with different denominators requires finding the LCM first. These skills help us work with parts of things in real life.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which of the following is a proper fraction?
Q2.What is the simplest form of 8/12?
Q3.What is 1/3 + 1/6?
Q4.Which pair shows equivalent fractions?
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