What havewe discussed? A fraction is a number representing a partof a whole. The whole maybe a single object or agroup of objects. (Scroll down to continue …)
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Whenexpressing a situation of counting partsto write a fraction, itmust be ensured that allparts are equal.
In5/7, 5 iscalled the numerator and 7 iscalled the denominator.
Fractions can beshown on a number line.
Every fraction has a point associated with it onthe number line.
In a proper fraction, the numerator is less than the denominator.
Thefractions, where the numerator is greater than the denominator are called improper fractions.
An improper fraction can be written as a combination of a whole and a part, and such fraction then called mixed fractions.
Each proper or improper fraction has many equivalent fractions.
To find an equivalent fraction of a given fraction, we may multiply or divide boththe numerator andthe denominator ofthe given fraction by the samenumber.
A fraction issaid to bein the simplest (or lowest) formif its numerator and the denominator haveno common factor except 1.
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What havewe discussed? A fraction is a number representing a partof a whole. The whole maybe a single object or agroup of objects. (Scroll down to continue …)
Study Tools
Audio, Visual & Digital Content
Whenexpressing a situation of counting partsto write a fraction, itmust be ensured that allparts are equal.
In5/7, 5 iscalled the numerator and 7 iscalled the denominator.
Fractions can beshown on a number line.
Every fraction has a point associated with it onthe number line.
In a proper fraction, the numerator is less than the denominator.
Thefractions, where the numerator is greater than the denominator are called improper fractions.
An improper fraction can be written as a combination of a whole and a part, and such fraction then called mixed fractions.
Each proper or improper fraction has many equivalent fractions.
To find an equivalent fraction of a given fraction, we may multiply or divide boththe numerator andthe denominator ofthe given fraction by the samenumber.
A fraction issaid to bein the simplest (or lowest) formif its numerator and the denominator haveno common factor except 1.
Hindi Version
Dig Deep
Topic Level Resources
Sub – Topics
Select A Topic
Topic:
Chapters Index
Select Another Chapter
[display-posts category=”CBSE 6 – Mathematics – Study – Premium” posts_per_page=”25″]
Product Of Numbers = Product Of LCM and GCD Of The Numbers
Addition of fractions
LCM (Least Common Multiple)
Rewriting fractions with a common denominator
Subtraction Of Fractions:
Multiplication Of Fractions:
Division Of Fractions
Fractions And Decimals
Introduction to Fractions
Fraction is the representation of the considered number of equal parts out of the total equal parts.
Example: ½. ⅔, 3/2 etc.
We use fractions at different situations such as:
Case 1:
When a single whole item is divided into more than one equal part.
Case 2:
Two or more whole items are divided into more than two equal parts.
This is the special case of addition or subtraction of case 1.
Etymology of Fractions:
The word “fraction” comes from Latin, where “fractus” means “broken.” It’s like breaking something into smaller pieces.
Representation of A Fraction:
A Fraction has the following three parts:
Parts of a Fraction:
A fraction consists of three parts:
Numerator: The upper part of the fraction, representing the selected or shaded sections.
Denominator: The lower part, indicating the total number of parts into which the whole is divided.
Fraction Bar Or Division Line: Fraction Bar Or Division Line is a bar that separates the numerator and denominator.
Example: If we have the fraction 3/4, then 3 is the numerator, and 4 is the denominator.
Rational number:
Rational number is a number used to represent a fraction.
In other words, Fraction is a numerical representation of the considered number of equal parts out of the total equal parts.
A Rational Number is represented as a numerator parts out of the denominator parts.
Examples:
Half (1/2):
Imagine cutting an apple into two equal parts. Each part represents a half of the apple.
One Third (1/3):
Divide a chocolate bar into three equal pieces. Each piece is a third of the whole chocolate.
Quarter (1/4):
Cut a sandwich into four equal parts. Each part is a quarter of the sandwich.
Types of Fractions:
Proper Fraction:
The numerator is smaller than the denominator (e.g., 2/5).
Improper Fraction:
The numerator is equal to or greater than the denominator (e.g., 7/4).
Mixed Fraction:
Combines a whole number and a proper fraction (e.g., 1 3/4).
Like Fractions:
Have the same denominators (e.g., 3/5 and 2/5).
Unlike Fractions:
Have different denominators (e.g., 1/3 and 2/5).
Equivalent Fractions:
Represent the same portion of a whole (e.g., 1/2 and 2/4).
Unit Fraction:
A unit fraction has a numerator of 1 (e.g., 1/3, 1/5).
It represents one equal part out of the whole.
Visualizing Fractions on a Number Line:
Place fractions on a number line to understand their relative positions.
For example, 1/2 lies exactly halfway between 0 and 1.
Operations with Fractions:
Addition Of Fractions:
Adding Fractions: A Step-by-Step Guide
Check the Denominators:
First, make sure the denominators (the bottom numbers) are the same for both fractions.
If they already have the same denominator, you’re dealing with like fractions.
Example: Adding 1/4 + 2/4 (both have a denominator of 4).
Add the Numerators:
The numerator is the number on top of the fraction.
Simply add the numerators together, just like you would with regular whole numbers.
Example:
1/4 + 2/4 = 3/4 (3 = 1 + 2)
Place the New Numerator Over the Common Denominator:
Take the sum of the numerators and place it on top of the fraction.
The denominator remains the same (don’t add the denominators together).
Example:
1/4 + 2/4 = 3/4 (numerator = 3, denominator = 4)
Simplify the Fraction (if Possible):
If the numerator and denominator have a common factor, divide both by that factor to simplify the fraction.
Example:
9/8 (from 3/8 + 2/8 + 4/8) can be simplified to 1 1/8.
Remember, adding fractions is like sharing and combining parts of a whole. Practice these steps, and soon you’ll be a pro at adding all types of fractions!
Create step by step Proces of addition of Fractions.
Multiplying Fractions: A Step-by-Step Guide
Multiply the Numerators:
Start by multiplying the numerators (the top numbers) of the fractions.
Example: Multiply 3/4 by 2/5.
Numerator product: (3 \times 2 = 6).
Multiply the Denominators:
Next, multiply the denominators (the bottom numbers) of the fractions.
Example: Multiply 3/4 by 2/5.
Denominator product: (4 \times 5 = 20).
Combine the Results:
Place the numerator product over the denominator product to form the new fraction.
Example: Multiply 3/4 by 2/5.
Result: \(\frac{6}{20}\)
Simplify (if Needed):
To simplify the fraction, find the greatest common factor (GCF) of the numerator and denominator.
Divide both the numerator and denominator by the GCF.
Example: Simplify \(\frac{6}{20}\)
GCF of 6 and 20 is 2.
Simplified result \(\frac{3}{10}\)
Remember, multiplying fractions is like finding the area of a part of a whole. Practice these steps, and soon you’ll be a pro at multiplying fractions!
Division Of Fractions:
Dividing fractions
Dividing fractions is the same as multiplying by the reciprocal (inverse).
Dividing Fractions: A Step-by-Step Guide
Check the Denominators:
First, take the reciprocal (flip) of the second fraction (the divisor).
Example: If you’re dividing (\frac{3}{4}) by (\frac{2}{5}), the reciprocal of (\frac{2}{5}) is (\frac{5}{2}).
Multiply the Numerators:
Multiply the numerators (the top numbers) of both fractions.
Example:
Numerator product: (3 \times 5 = 15).
Multiply the Denominators:
Multiply the denominators (the bottom numbers) of both fractions.
Example:
Denominator product: (4 \times 2 = 8).
Form the Resultant Fraction:
Place the numerator product over the denominator product.
Example:
Result: (\frac{15}{8}).
Simplify (if Needed):
If possible, simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator.
Example:
Simplified result: (\frac{15}{8}) can be expressed as (\frac{1}{\frac{8}{15}}).
Remember, dividing fractions is like sharing parts of a whole. Practice these steps, and soon you’ll be a pro at dividing fractions!
Properties of Fractions:
Fractions share properties similar to real numbers:
Commutative and Associative Properties hold true for fractional addition and multiplication.
The identity element for fractional addition is 0, and for multiplication, it’s 1.
