# CLASS-6INTRODUCTION OF FRACTION

FRACTION -

Fractions are a way of representing numbers that are not whole numbers. They consist of two parts: the numerator and the denominator, separated by a horizontal line, which is called a fraction bar. The numerator represents the number of equal parts you have, while the denominator represents the total number of equal parts that make up the whole. A fraction consists of two parts: a numerator and a denominator. The numerator is the number above the fraction line, and the denominator is the number below it.

The general format of a fraction is:-

Numerator
---------------
Denominator

For example, in the fraction 3/4:

• The numerator is 3, which means there are 3 equal parts.
• The denominator is 4, which means the whole is divided into 4 equal parts.
• 1/2: One-half (1 divided by 2)
• 3/4: Three-fourths (3 divided by 4)
• 5/8: Five-eighths (5 divided by 8)
• 2/3: Two-thirds (2 divided by 3)

Fractions can represent parts of a whole or parts of a collection. When the numerator is smaller than the denominator (e.g., 1/2 or 3/4), the value of the fraction is less than one, representing a proper fraction. If the numerator is equal to or greater than the denominator (e.g., 5/4 or 7/7), the value is greater than one, and it is called an improper fraction.

Converting between fractions and decimals: Fractions can also be represented as decimals. To convert a fraction to a decimal, you perform the division. For example, to convert 3/4 to a decimal, you divide 3 by 4,

3 รท 4 = 0.75.

Arithmetic operations with fractions :-

You can perform arithmetic operations (addition, subtraction, multiplication, and division) with fractions, but it often involves finding a common denominator. For example:

• Adding fractions:- To add fractions, they should have the same denominator. If they don't, you need to find a common denominator before adding them together.
• Subtracting fractions:- Similar to addition, you need a common denominator before subtracting fractions.
• Multiplying fractions:- To multiply fractions, you simply multiply the numerators together and the denominators together.
• Dividing fractions:- To divide fractions, you invert the second fraction (i.e., swap the numerator and denominator) and then multiply the two fractions.

Working with fractions can be a valuable skill in various areas, such as cooking, woodworking, and mathematics. Understanding fractions allows you to express precise measurements and proportions in a concise way.

The fraction 3/4 can be visually represented as:

3

---------

4

Here are some key terms related to fractions:

1. Proper Fraction:- A fraction where the numerator is smaller than the denominator (e.g., 1/2 or 3/5).
2. Improper Fraction:- A fraction where the numerator is equal to or greater than the denominator (e.g., 5/4 or 7/3).
3. Mixed Number:- A combination of a whole number and a proper fraction (e.g., 1/2 or 3/4).
4. Equivalent Fractions:- Fractions that represent the same quantity but have different numerators and denominators (e.g., 1/2 and 2/4 are equivalent).
5. Simplifying or Reducing:- Expressing a fraction in its simplest form by dividing both the numerator and denominator by their greatest common divisor.
6. Adding and Subtracting Fractions:- To add or subtract fractions, their denominators must be the same. If they are not the same, you need to find a common denominator before performing the operation.
7. Multiplying and Dividing Fractions:- To multiply fractions, you simply multiply the numerators and denominators separately. To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.