CBSE Class 6 Mathematics Fractions Chapter Notes

CBSE Class 6 Fractions Chapter Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Fractions

7.1 Fractions

A fraction is part of an entire object.

7.2 Types of Fraction

We can define the three types of fractions like this:

7.3 Equivalent Fraction

Equivalent fractions are fractions that have the same value or represent the same part of an object. If a pie is cut into two pieces, each piece is also one-half of the pie. If a pie is cut into 4 pieces, then two pieces represent the same amount of pie that 1/2 did. We say that 1/2 is equivalent to 2/4.

Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication. For example if we compare 1/2 and 2/4, we would multiply 1/2 by 2/2 which would result in 2/4 so they are equivalent.

To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since 3/6 is not the same as 3/7, the fractions are not equivalent.

· Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ...

· Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...

· Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ...

· Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...

· Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...

7.4 Simplest form of a Fraction

Fractions may have numerators and denominators that are composite numbers (numbers that has more factors than 1 and itself).

How to simplify a fraction:

· Find a common factor of the numerator and denominator. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.

· Divide both the numerator and denominator by the common factor.

· Repeat this process until there are no more common factors.

· The fraction is simplified when no more common factors exist.

Another method to simplify a fraction

· Find the Greatest Common Factor (GCF) of the numerator and denominator

· Divide the numerator and the denominator by the GCF

7.5 Comparing Fractions

Comparing Fractions with the Same Denominator

A Fraction consists of two numbers separated by a line. The top number (or numerator) tells how many fractional pieces there are. In the fraction 3/8, we have three pieces. The denominator of a fraction tells how many pieces an object was divided into. The fraction 3/8 tells us that the whole object was divided into 8 pieces.

If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction. For example 5/8 is larger than 3/8 because all of the pieces are the same and five pieces are more than three pieces.

Comparing Fractions with Different Denominators

A Fraction consists of two numbers separated by a line. The top number (or numerator) tells how many fractional pieces there are. The fraction 3/8 indicates that there are three pieces. The denominator of a fraction tells how many pieces an object was divided into. The fraction 3/8 indicates that the whole object was divided into 8 pieces. 

If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction.

For example 5/8 is larger than 5/16 because each fraction says there are five pieces but if an object is divided into 8 pieces, each piece will be larger than if the object were divided into 16 pieces. Therefore, five larger pieces are more than five smaller pieces.

Comparing Unlike Fractions

If two fractions have different numerators and denominators it is difficult to determine which fraction is larger. It is easier to determine which is larger if both fractions have the same denominator.

Multiply the numerator and denominator of one fraction by the same number so both fractions will have the same denominator. For example, if 5/12 and 1/3 are being compared, 1/3 should be multiplied by 4/4. It does not change the value of 1/3 to be multiplied by 4/4 (which is equal to 1) because any number multiplied by 1 is still the same number. After the multiplication (1/3 * 4/4 = 4/12), the comparison can be made between 5/12 and 4/12.

You may have to multiply both fractions by different numbers to produce the same denominator for both fractions. For example if 2/3 and 3/4 are compared, we need to multiply 2/3 by 4/4 to give 8/12 and multiply 3/4 by 3/3 to give 9/12. The fraction 3/4 which is equal to 9/12 is larger than 2/3 which is equal to 8/12. The fraction with the larger numerator is the larger fraction if the denominators are the same.\

7.6 Addition of Fractions

Adding Fractions with the Same Denominator

Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.

  n u m e r a t o r  
d e n o m i n a t o r 

To add two fractions with the same denominator, add the numerators and place that sum over the common denominator.

Adding Fractions with Different Denominators

How to Add Fractions with different denominators:

• Find the Least Common Multiple (LCM) of the denominators of the fractions

• Rename the fractions to have the LCM

• Add the numerators of the fractions

• Simplify the Fraction

Example: Find the Sum of 2/9 and 3/1

• Determine the Least Common Multiple of 9 and 12 which is 36

• Rename the fractions to use the Least Common Multiple (2/9 = 8/36, 3/12 = 9/36)

• The result is 8/36 + 9/36

• Add the numerators and put the sum over the LCM = 17/36

• Simplify the fraction if possible. In this case it is not possible

Adding Mixed Numbers with the Same Denominator

Mixed numbers consist of an integer followed by a fraction.

How to add two mixed numbers whose fractions have the same denominator:

• Add the numerators of the two fractions

• Place that sum over the common denominator.

• If this fraction is improper (numerator larger than or equal to the denominator) then convert it to a mixed number

• Add the integer portions of the two mixed numbers

• If adding the fractional parts created a mixed number then add its integer portion to the sum.

Example: 3 2/3 + 5 2/3 =

How to add two mixed numbers whose fractions have different denominator:

• Add the fractional part and whole part of the two fractions separately.

• If the addition of fractional part is improper (numerator larger than or equal to the denominator) then convert it to a mixed number

• Add the integer portions of the two mixed numbers

• If adding the fractional parts created a mixed number then add its integer portion to the sum.

Example: 3 1/2 + 5 2/3 =

7.7 Subtraction of Fractions

Subtracting Fractions with the Same Denominator

Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.

  n u m e r a t o r  
d e n o m i n a t o r

To subtract two fractions with the same denominator, subtract the numerators and place that difference over the common denominator.

Subtracting Fractions with Different Denominators

To Subtract Fractions with different denominators:

• Find the Least Common Multiple (LCM) of the denominators of the fractions

• Rename the fractions to have the LCM

• Subtract the numerators of the fractions

• The difference will be the numerator and the LCD will be the denominator of the answer.

• Simplify the Fraction

Example: Find the difference between 3/12 and 2/9.

• Determine the Least Common Multiple of 9 and 12 which is 36

• Rename the fractions to use the Least Common Multiple (2/9 = 8/36, 3/12 = 9/36)

• The result is 9/36 - 8/36

• Subtract the numerators and put the difference over the LCM = 1/36

• Simplify the fraction if possible. In this case it is not possible

Mixed Numbers Consist of an Integer Followed by a Fraction.

How to subtract mixed numbers having the same denominator:

• Make the first numerator larger than the second if it is not.

• Subtract the second numerator from the first

• Place that difference over the common denominator.

• Subtract the integer portions of the two mixed numbers

• State the answer

Example: 5 1/3 - 3 2/3 =

How to subtract two mixed numbers whose fractions have different denominator:

• Subtract the fractional part and whole part of the two fractions separately.

• If the subtraction of fractional part is improper (numerator larger than or equal to the denominator) then convert it to a mixed number

• Subtract the integer portions of the two mixed numbers

•  If subtracting the fractional parts created a mixed number then subtract its integer portion to the sum.

Example: 3 ½ - 5 2/3 =

How to subtract two mixed numbers whose fractions have different denominator:

• Subtract the fractional part and whole part of the two fractions separately.

• If the subtraction of fractional part is improper (numerator larger than or equal to the denominator) then convert it to a mixed number

• Subtract the integer portions of the two mixed numbers

• If subtracting the fractional parts created a mixed number then subtract its integer portion to the sum.

Example: 3 ½ - 5 2/3 =

Please click on below link to download pdf file for CBSE Class 6 Fractions Chapter Concepts.