CBSE Class 6 Maths Revision Notes Chapter 7

CBSE Class 6 Mathematics Chapter 7 Revision Notes – Fractions

After getting familiar with whole numbers in the second chapter, it is now time to understand the concept of fractions. This is an important chapter as the students will learn the basic concepts that differentiate fractions from other numbers. Class 6 Mathematics Chapter 7 Notes are prepared by subject experts at Extramarks to help students gain conceptual clarity about the topic. These notes will also help students revise the chapter quickly and effectively.

Access Class 6 Mathematics Chapter 7 – Notes on Fraction 

Fractions: The Basic Concepts

Fractions

  • A fraction is not a whole number.
  • It is a numerical quantity that represents a part of a whole.
  • A ratio of two numbers can be presented as a fraction.
  • The quantity of the upper part of the solidus is called the numerator.
  • And the quantity of the lower part of the solidus is known as the denominator.
  • For example, in the given fraction 23 , 2 is the numerator and 3 is the denominator. It is read as two-thirds.

Fractions on the Number Line

  • Like whole numbers, fractions can also be placed on a number line.
  • Suppose, 45 is a given fraction. Its value is 0.8. Therefore, the fraction is greater than zero but smaller than one. So, the fraction lies between zero and one on the number line.
  • The fraction is read as four-fifths.

Types of Fractions

  • Like fractions 
  • Unlike fractions
  • Proper fractions
  • Improper fractions
  • Mixed fractions
  • Equivalent fractions

Like Fractions

  • Fractions that have the same denominator are called the like fractions.
  • For example, fractions 15, 35, and 45 are like fractions as they have the same denominator 5.

Unlike Fractions

  • Unlike fractions are those fractions which have a different denominator.
  • For example, 23, 45, 16 are all unlike fractions.

Proper Fractions

  • Proper fractions are those fractions which have a smaller numerator and a greater denominator.
  • For example, 311 is a proper fraction.

Improper Fractions

  • This kind of fraction has a greater numerator and a smaller denominator.
  • 103 is an example of an improper fraction.

Mixed Fractions

  • If the fraction 113 is simplified, it can be expressed as a combination of a whole number and a fraction, that is, 323.
  • 3 is the whole number whereas 23 is a proper fraction.
  • Therefore, a mixed fraction is an improper fraction expressed as a combination of a whole number and a proper fraction.
  • A mixed fraction is also known as an incorrect fraction.

Equivalent Fractions

  • The numerator and the denominator of a fraction can be multiplied or divided by the same number.
  • The result gives an equivalent fraction.
  • For example, 39= 3 ÷39 ÷3 = 13.
  • The result gives the lowest form of a fraction as the numerator and the denominator have no common factor except 1.

Comparing Unlike Fractions

  • When the denominators are the same:
  • The fraction with the greater numerator is considered the greater fraction.
  • For example, 9/5 is greater than 3/5.
  • When the numerator is the same:
  • The fraction with the smaller denominator is the greater one.
  • For example, if 5/6 and 5/2 are compared, the latter becomes the greater fraction.

Addition or Subtraction of Mixed Fractions

  • Method I: Add or subtract the whole numbers separately and perform the same operation for the fraction part separately.
  • For example, consider 223 and 415 given fractions to be added.
  • The whole numbers are 2 and 3.
  • 223 + 415 = 2 + 23 + 4 + 15 = 6 +  23 +  15   ……… (i)
  • 23 +  15  = 2×53×5 + 1×33×5 = 1015 + 315 = 1315   ………. (ii)
  • 1315 can be written as 15-215= 1 – 215
  • If (i) and (ii) are added, 6 + 1315 = 6 + 1 – 215 = 7 – 215 = 7×15-215 = 10315
  • Therefore, 223 + 415=10315
  • Method II: The alternative method of adding or subtracting is to convert the mixed fractions into improper fractions and add or subtract them directly.
  • For example, take the same fractions for a better understanding.
  • 223 = 83
  • 415 = 215
  • Add 83 and 215 directly. 83+215 = (8×5)+(21×3)3×5 [since LCM of the denominators is 15].
  • 40+6315 = 10315
  • Therefore, 223 + 415=10315.

FAQs (Frequently Asked Questions)

A fraction can be defined as a portion of a whole number. Fractions can be expressed in the form of a ratio of two numbers. The numbers of the upper part and lower part are known as the numerator and denominator respectively. Fractions are an important part of the number system. So, students must understand  them very well. Students can access the notes on fractions on the Extramarks’ website.

When the denominators of the given fractions are the same then the fraction with the greater numerator is considered the greater fraction. But if the numerators are the same and the denominators are different, then the fraction with the greater denominator is regarded as the smaller fraction. If no similarity is found between the fractions then they must be converted into like fractions for further comparison.

The fraction with  a smaller numerator and larger denominator is called a proper fraction. These fractions are always less than 1. The improper fraction, on the other hand, has a numerator greater than the denominator. Such fractions will always be more than 1 in value. The mixed fractions contain one whole number and a fractional part.

To obtain an equivalent fraction, both the numerator and the denominator must be divided or multiplied by the same integer.

For example, 12 is a proper fraction. If the fraction is multiplied by 2, the new fraction 24 becomes its equivalent fraction.

714 is a fraction which, when divided by 7, gives an equivalent fraction 12, i.e., 714 = 7÷714÷7 = 12.

Two fractions can have the same denominator or different denominators. When the denominators are the same, then addition becomes easy. Keep the denominator unchanged and add only the numerators. For example, 2/5 + 4/5 = 6/5.

When the fractions have different denominators, the first step is to have  the same denominator. The fractions need to be converted into like fractions by taking the LCM of the denominators. Then follow the method of addition of like fractions.