Processing math: 100%

Addition and Subtraction of Like Fractions

Here we will learn about addition and subtraction of like fractions.

Addition of Like Fractions:

In order to add two or more like fractions, we may follow the following steps:

Step I:

Obtain the fractions.

Step II:

Add the numerators of all fractions.


Step III:

Retain the common denominator of all fractions.


Step IV:

Write the fraction as Result in Step II / Result in Step III.




For Example:

Add the following fractions.

1. 1/6 + 4/6

Solution:

We have,

1/6 + 4/6

= (1+4)/6

= 5/6



2. 2/7 + 3/7 + 4/7

Solution:

We have,

2/7 + 3/7 + 4/7

= (2+3+4)/7

= 9/7



3. 23/5 + 4/5 + 12/5

Solution:

We have,

23/5 + 4/5 + 12/5

= (2 × 5 + 3)/5 + 4/5 + (1 × 5 + 2)/5

= (10 + 3)/5 + 4/5 + (5 + 2)/5

= 13/5 + 4/5 + 7/5

= (13 + 4 + 7)/5

= 24/5



4. 11/4 + 23/4 + 71/4

Solution:

We have,

11/4 + 23/4 + 71/4

= (1 × 4 + 1)/4 + (2 × 4 + 3)/4 + (7 × 4 + 1)/4

= (4 + 1)/4 + (8 + 3)/4 + (28 + 1)/4

= 5/4 + 11/4 + 29/4

= (5 + 11 + 29)/4

= 45/4


Subtraction of Like Fractions:

To subtract two or more like fractions we simply subtract their numerators and keep the same denominator.



In order to subtract two like fractions, we may follow the following steps:



Step I:

Obtain the two fractions and their numerators.



Step II:

Subtract the smaller numerator from the bigger numerator.



Step III:

Retain the common denominator.



Step IV:

Write the fraction as Result in Step II / Result in Step III.



For Example:

1. Subtract 3/10 from 8/10

Solution:

We have to find,

8/10 – 3/10

= (8 – 3)/10

= 5/10

= (5 ÷ 5)/(10 ÷ 5) [Dividing the numerator and denominator by their HCF (highest common factor) 5].

= 1/2



2. Compute: 5/12 – 7/12 + 11/12

Solution:

We have,

5/12 – 7/12 + 11/12

= (5-7+11)/12

= (11-2)/12

= 9/12

= (9 ÷ 3)/(12 ÷ 3) [Dividing the numerator and denominator by their HCF (highest common factor) 3].

= 3/4



3. Simplify: 42/3 + 1/3 – 41/3

Solution:

We have,

42/3 + 1/3 – 41/3

= (4 × 3 + 2)/3 + 1/3 - (4 × 3 + 1)/3

= (12+2)/3 + 1/3 – (12+1)/3

= 14/3 + 1/3 - 13/3

= (14 + 1 – 13)/3

= (15 – 13)/3

= 2/3

4. Subtract 37 from 57.

Solution:

57 - 37

= 5−37

= 27


5. Emily has 712 hrs to reach her school. She takes 512 hrs to finish her breakfast. How much time is left with Emily to reach her school?

Solution:

We subtract 512 from 712.

712 - 512

= 7−512

= 212 hrs is left with her.



For Example:

Add the following fractions.

1. 1/6 + 4/6

Solution:

We have,

1/6 + 4/6

= (1+4)/6

= 5/6



2. 2/7 + 3/7 + 4/7

Solution:

We have,

2/7 + 3/7 + 4/7

= (2+3+4)/7

= 9/7



3. 23/5 + 4/5 + 12/5

Solution:

We have,

23/5 + 4/5 + 12/5

= (2 × 5 + 3)/5 + 4/5 + (1 × 5 + 2)/5

= (10 + 3)/5 + 4/5 + (5 + 2)/5

= 13/5 + 4/5 + 7/5

= (13 + 4 + 7)/5

= 24/5

Addition and Subtraction of Like Fractions


4. 11/4 + 23/4 + 71/4

Solution:

We have,

11/4 + 23/4 + 71/4

= (1 × 4 + 1)/4 + (2 × 4 + 3)/4 + (7 × 4 + 1)/4

= (4 + 1)/4 + (8 + 3)/4 + (28 + 1)/4

= 5/4 + 11/4 + 29/4

= (5 + 11 + 29)/4

= 45/4

● Fraction

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Interesting Fact about Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions







Numbers Page

6th Grade Page

From Addition and Subtraction of Like Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

RSS

  1. Multiplication by Ten, Hundred and Thousand |Multiply by 10, 100 &1000

    May 01, 25 11:57 PM

    Multiply by 10
    To multiply a number by 10, 100, or 1000 we need to count the number of zeroes in the multiplier and write the same number of zeroes to the right of the multiplicand. Rules for the multiplication by 1…

    Read More

  2. Adding and Subtracting Large Decimals | Examples | Worksheet | Answers

    May 01, 25 03:01 PM

    Here we will learn adding and subtracting large decimals. We have already learnt how to add and subtract smaller decimals. Now we will consider some examples involving larger decimals.

    Read More

  3. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  4. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  5. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More