Addition and Subtraction of Unlike Fractions

In addition and subtraction of unlike fractions, we first convert them into corresponding equivalent like fractions and then they are added or subtracted.


Following steps are used to do the same.

Step I:

Obtain the fractions and their denominators.


Step II:

Find the LCM (least common multiple) of the denominators.


Step III:

Convert each fraction into an equivalent fraction having its denominator equal to the LCM (least common multiple) obtained in Step II.

Step IV:

Add or subtract like fractions obtained in Step III.



For Example:

1. Add ²/₃ and ³/₇.

Solution:

The LCM (least common multiple) of the denominators 3 and 7 is 21.



So, we convert the given fractions into equivalent fractions with denominator 21.

We have,

2/3 + 3/7

= (2 × 7)/(3 × 7) + (3 × 3)/(7 × 3)

[since 21 ÷ 3 = 7 and 21 ÷ 7 = 3]

= 14/21 + 9/21

= (14 + 9)/21

= 23/21




2. 1/6 + 3/8

Solution:

The LCM (least common multiple) of the denominators 6 and 8 is 24.



So, we convert the given fractions into equivalent fractions with denominator 24.

We have,

= 1/6 = (1 × 4)/(6 × 4)= 4/24 [since 24 ÷ 6 = 4]

and, 3/8 = (3 × 3)/(8 × 3) = 9/24 [since 24 ÷ 8 = 3]

Thus, 1/6 + 3/8 = 4/24 + 9/24

= (4 + 9)/24

= 13/24




3. Add 24/5 and 35/6.

Solution:

We have,

24/5 = (2 × 5 + 4)/5 = (10 + 4)/5 = 14/5

and, 35/6 = (3 × 6 + 5)/6 = 23/6

Now, we will compute 14/5 + 23/6


The LCM (least common multiple) of the denominators 5 and 6 is 30.



So, we convert the given fractions into equivalent fractions with denominator 30.

We have,

= 14/5 = (14 × 6)/(5 × 6) = 84/30 [since 30 ÷ 5 = 6]

and, 23/6 = (23 × 5)/(6 × 5) = 115/30 [since 30 ÷ 6 = 5]

Thus, 14/5 + 23/6 = 84/30 + 115/30

= (84 + 115)/30

= 199/30



= 6¹⁹/₃₀





4. Find the difference of ¹⁷/₂₄ and ¹⁵/₁₆.

Solution:

The LCM (least common multiple) of the denominators 24 and 16 is 48.



[Therefore, LCM = 2 × 2 × 2 × 2 × 3 = 48]

So, we convert the given fractions into equivalent fractions with denominator 48.

We have,

= 17/24 = (17 × 2)/(24 × 2) = 34/48 [since 48 ÷ 24 = 2]

and, 15/16 = (15 × 3)/(16 × 3) = 45/48 [since 48 ÷ 16 = 3]

Clearly, 45/48 > 34/48

Therefore, 15/16 > 17/24

Hence, difference = 15/1617/24

= 45/4834/48

= (45 – 34)/48

= 11/48.




5. Simplify: 42/3 – 31/4 + 2 1/6

Solution:

We have,

42/3 – 31/4 + 21/6

= (4 × 3 + 2)/3(3 × 4 + 1)/4 + (2 × 6 +1)/6

= (12 + 2)/3(12 +1)/4 + (12+1)/6

= 14/313/4 + 13/6


The LCM (least common multiple) of the denominators 3, 4 and 6 is 12.

[Therefore, LCM = 2 × 2 × 3 = 12]

So, we convert the given fractions into equivalent fractions with denominator 12.

We have,

= (14 × 4)/(3 × 4)(13 × 3)/(4 × 3) + (13 × 2)/(6 × 2)

= 56/1239/12 + 26/12

= (56 – 39 + 26)/12

= (82 – 39)/12

= 43/12



= 3⁷/₁₂



● 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 Unlike 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

  1. Successor and Predecessor | Successor of a Whole Number | Predecessor

    Jul 29, 25 12:59 AM

    Successor and Predecessor
    The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number…

    Read More

  2. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  3. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  4. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  5. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More