Fractions - Vulgar Fractions : Fractions with equal denominator (like fractions), fractions with unequal denominator (unlike fractions), order relation (comparing), ascending and descending order, addition, subtraction, and multiplication of fractions.
Introduction
Vulgar fractions represent parts of a whole where the numbers are written as a numerator over a denominator.
Explanation Step by Step
A fraction has two parts: the Numerator (top number) which shows parts taken, and the Denominator (bottom number) which shows total equal parts.
Sub-topics
Like and Unlike Fractions
Fractions with the same denominator are called Like Fractions. Fractions with different denominators are called Unlike Fractions.
| Type | Property | Example |
|---|---|---|
| Like Fractions | Same Denominator | 4/9, 2/9, 7/9 |
| Unlike Fractions | Different Denominators | 1/2, 3/5, 4/7 |
Examples
Example 1: Comparison
Compare 7/12 and 5/12.
Since denominators are same, compare numerators 7 and 5.
Result: 7/12 > 5/12
Tricks and Shortcuts
If Numerators are same: The fraction with the smaller denominator is the larger fraction. Example: 5/2 > 5/10.
Common Mistakes
Adding denominators during addition (e.g., 2/5 + 1/5 = 3/10 is WRONG). Only add the numerators.
Practice Questions
Easy Questions
- Identify the numerator in 5/9.
- Add: 4/15 + 7/15.
- Subtract: 9/10 - 3/10.
Medium Questions
- Arrange in Ascending Order: 5/11, 2/11, 8/11, 1/11.
- Which is greater: 4/7 or 4/9?
- Find the missing number: 3/14 + ?/14 = 10/14.
Hard Questions
- If a cake is divided into 8 parts and 3 parts are eaten, what fraction remains?
- Order from greatest to smallest: 7/2, 7/5, 7/8, 7/3.
- Subtract the sum of 1/12 and 3/12 from 11/12.
Revision Summary
Always keep denominators same during addition/subtraction of like fractions. Use numerators to determine the order of like fractions.
What is the ascending order of the fractions 3/10, 1/2, 7/20?
A
3/10, 7/20, 1/2
B
1/2, 7/20, 3/10
C
7/20, 3/10, 1/2
D
3/10, 1/2, 7/20