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# Fractions Class 6 Notes CBSE Maths Chapter 7 (Free PDF Download)

Last updated date: 20th Sep 2024
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## Revision Notes for CBSE Class 6 Maths Chapter 7 - Free PDF Download

Free PDF download of Class 6 Maths Chapter 7 - Fractions Revision Notes & Short Key-notes prepared by expert Maths teachers from the latest edition of CBSE(NCERT) books. To register Maths Tuitions on Vedantu.com to clear your doubts.

You can also register Online for NCERT Class 6 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for the better solutions ,they can download Class 6 Maths NCERT Solutions to help you to revise complete syllabus and score more marks in your examinations.

## Access Class 6 Mathematics Chapter 7 – Fractions Notes in 30 Minutes

What have we discussed?

• A fraction is a number that represents a portion of something larger.

• A single object or a group of objects might make up the whole.

• It is necessary to guarantee that all parts are equal when stating a circumstance of counting components to write a fraction.

• As in example  $\dfrac{8}{3}$ , the numerator in this equation is $8$ and the denominator is $3$.

Fraction on the Number Line:

• A number line can be used to display fractions.

• Every fraction has a number line point connected with it.

• For example, how can we  $\dfrac{9}{7}$ on a number line?

Solution:

The value of $\dfrac{9}{7}$ is $1.23$ which means that $\dfrac{9}{7}$ lies between $1$ and $2$ . We can show this on a number is as follows;

Like fractions are those that have the same denominator.

For example, $\dfrac{9}{30},\dfrac{5}{30},\dfrac{1}{30}$ are the like fractions.

Unlike fractions are fractions having different denominators.

For example, $\dfrac{3}{56},\dfrac{2}{30},\dfrac{8}{5}$ are the unlike fractions.

Proper Fraction:

• A proper fraction is a fraction that represents a portion of a whole.

• The numerator of a proper fraction is less than the denominator.

• For example, $\dfrac{3}{5},\dfrac{7}{30},\dfrac{6}{5}$ are the proper fractions.

Improper Fraction:

• Improper fractions are those in which the numerator is higher than the denominator.

• When an improper fraction is stated as a mixture of a whole and a part, it is referred to as a mixed fraction.

• There are several equivalent fractions for each right or improper fraction.

• A mixed fraction can be expressed as an incorrect fraction in the following way:

$\dfrac{\left( \text{Whole }\!\!\times\!\!\text{ Denominator} \right)\text{ + Numerator}}{\text{Denominator}}$

• For example,  $4\dfrac{2}{5},3\dfrac{1}{9},12\dfrac{7}{8}$ are the improper fractions.

We can multiply or divide both the numerator and the denominator of a given fraction by the same number to discover an equal fraction.

For example, Equivalent fraction of $\dfrac{14}{56}$ is;

$\dfrac{14}{56}=\dfrac{14\div 14}{56\div 14}$

$\dfrac{14}{56}=\dfrac{1}{4}$

If the numerator and denominator of a fraction have no common factor except $1$ , it is said to be in the simplest (or lowest) form.

When adding or subtracting fractions, the $LCM$of the denominators is selected as the common denominator.

Comparing Unlike Fractions:

• The fraction with the greater numerator is greater when two fractions have the same denominator.

For example, if we compare $\dfrac{9}{3}$ and $\dfrac{4}{3}$ fractions, we can conclude that

$\dfrac{9}{3}>\dfrac{4}{3}$

That is

$\Rightarrow \dfrac{9}{3}>\dfrac{4}{3}$

$\Rightarrow 3>1.33$

• When the numerator is the same in two fractions then, the fraction with the smaller denominator is greater of the two.

For example, if we compare $\dfrac{7}{6}$ and $\dfrac{7}{3}$ fractions, we can conclude that $\dfrac{7}{6}<\dfrac{7}{3}$

That is

$\Rightarrow \dfrac{7}{6}<\dfrac{7}{3}$

$\Rightarrow 1.16<2.33$

How do we add or subtract mixed fractions?

• Mixed fractions can be expressed as a whole portion plus a proper fraction or as an improper fraction in its entirety.

• One method of adding (or subtracting) mixed fractions is to do the operation separately for each of the whole parts.

• The alternative method is to write the mixed fractions as improper fractions and then add (or subtract) them directly.

• Example:

$4\dfrac{2}{3}+3\dfrac{1}{4}$ , We will solve the given example by applying both the methods.

Solution:

Method $I$:

$\text{4}\dfrac{\text{2}}{\text{3}}\text{+3}\dfrac{\text{1}}{\text{4}}\text{ = 4+}\dfrac{\text{2}}{\text{3}}\text{+3+}\dfrac{\text{1}}{\text{4}}$

$\text{4}\dfrac{\text{2}}{\text{3}}\text{+3}\dfrac{\text{1}}{\text{4}}\text{ = 7+}\dfrac{\text{2}}{\text{3}}\text{+}\dfrac{\text{1}}{\text{4}}\text{ -----}\left( \text{1} \right)$

Here,

$~~\frac{2}{3}+\frac{1}{4}\text{ }=\text{ }\frac{2\text{ }\times \text{ }4}{3\text{ }\times \text{ }4}+\frac{1\text{ }\times \text{ }3}{4\text{ }\times \text{ }3}~~$

$~~~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }=\text{ }\frac{8}{12}+\frac{3}{12}~$

$~~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }=\frac{11}{12}$

$\dfrac{\text{11}}{\text{12}}$ can be written as;

$~\text{ }\frac{11}{12}~\text{ }=\text{ }\frac{12-1}{12}~$

$~\text{ }~\text{ }~\text{ }~\text{ }=\text{ }1\text{ }-\text{ }\frac{1}{12}~$

Therefore, equation $\left( 1 \right)$ becomes,

$~7+\frac{2}{3}+\frac{1}{4}\text{ }=\text{ }7\text{ }+\text{ }1-\frac{1}{12}~$

$~~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }=\text{ }8\text{ }-\text{ }\frac{1}{12}~~$

$~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }=\text{ }\frac{\left( 12\text{ }\times \text{ }8 \right)\text{ }-\text{ }1}{12}$

Therefore,

$~~7+\frac{2}{3}+\frac{1}{4}\text{ }=\text{ }\frac{96\text{ }-\text{ }1}{12}~$

$~7+\frac{2}{3}+\frac{1}{4}\text{ }=\text{ }\frac{95}{12}~$

Method $II$:

$\text{4}\dfrac{\text{2}}{\text{3}}\text{+3}\dfrac{\text{1}}{\text{4}}\text{ }$

$\text{4}\dfrac{\text{2}}{\text{3}}$ can be written as

$4\frac{2}{3}=\frac{\left( 4\times 3 \right)+2}{3}~~$

$~4\frac{2}{3}=\frac{12+2}{3}$

$4\frac{2}{3}=\frac{14}{3}$

$3\dfrac{1}{4}$ can be written as

$~~3\frac{1}{4}=\frac{\left( 3\times 4 \right)+1}{4}$

$~3\frac{1}{4}=\frac{12+1}{4}$

$~~3\frac{1}{4}=\frac{13}{4}~~$

Therefore,

$~7+\frac{2}{3}+\frac{1}{4}\text{ }=\text{ }\frac{14}{3}+\frac{13}{4}~~$

$~~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }=\text{ }\frac{\left( 14\text{ }\times \text{ }4 \right)+\left( 13\text{ }\times \text{ }3 \right)}{\left( 3\text{ }\times \text{ }4 \right)}~$

$~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }~\text{ }=\text{ }\frac{56+39}{12}$

Since,

$\left( \text{LCM of 3 and 4 = 12} \right)$

Therefore,

$\text{7+}\dfrac{\text{2}}{\text{3}}\text{+}\dfrac{\text{1}}{\text{4}}\text{ = }\dfrac{\text{95}}{\text{12}}$

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• Provides quick, clear summaries of key concepts.

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## Conclusion

For an enhanced comprehension of this subject, NCERT - Class 7 Math Chapter 7 Fractions thoughtfully prepared by experienced educators at Vedantu is your invaluable companion. These resources break down the complexities of Fractions into easily digestible sections, helping you grasp new concepts, (master formulas), and navigate through questions effortlessly. By immersing yourself in these materials, you not only prepare for your studies more efficiently but also develop a profound understanding of the subject matter.

## FAQs on Fractions Class 6 Notes CBSE Maths Chapter 7 (Free PDF Download)

Q1. What is a fraction according to Chapter 7 of Class 6 Maths?

A fraction can be defined as a part of the whole number. This Is expressed as the ratio of two integers. The upper part is the numerator and the below is the denominator. Fraction is an important chapter and students should study with proper focus and attention.  There will be numerous sums connected with this chapter so the proper understanding of the concept is very important. The detailed explanation can be referred to in Vedantu from NCERT solutions.

Q2. What are the topics covered in Chapter 7 of Class 6 Maths?

The topics are different types of a fraction like a proper fraction, improper fraction, mixed fraction, conversion of the mixed fraction to an improper fraction, conversion of the improper fraction to mixed fraction, representation of fraction on a number line, the simplest form of fractions, equivalent fractions, like and unlike fractions, comparison of fractions, addition and subtraction of fractions. These are the fundamentals of fractions and should be thorough with basic topics.

Q3. Define proper, improper and mixed fractions.

Proper fraction can be defined as the fraction where the numerator is less than the denominator. The fraction will always be less than one.

An improper fraction is defined as the fraction where the numerator is more than the denominator and the fraction will be more than one.

A mixed fraction is a combination of proper and improper fractions. These definitions are important and students should know the difference between different types of fractions and their conversions.

These solutions are available on Vedantu's official website(vedantu.com) and mobile app free of cost.

Q4. How do you add the fraction?

There is a procedure to add the fraction. Adding like fractions becomes easy as the denominator is the same for both the fractions. For example 1/7+2/7=3/7. It is very simple: you need to just add the numerator as the denominator is the same.

When you are adding unlike fractions then the denominator will be different. The first step is to make the fractions like fractions, which means, we have to make the denominator the same.

The, unlike fractions, is converted to like fractions by taking the LCM of the denominators. Once the fractions are like fractions then the addition is easy.

Q5. How do you subtract the fractions?

Subtraction of like fractions is easy. As we have done in the case of addiction we have to now just subtract the numerators in like fractions. Example 3/5-1/5=2/5

But in the case of unlike fractions, the procedure is not the same as the denominators are different; we cannot simply subtract the numerators.  Next, We have to convert unlike fractions to like fractions. The, unlike fractions, should be changed to like fractions by taking the LCM of the denominators. Once the fractions are like fractions then subtract the numerators.