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 = 15/16 – 17/24
= 45/48 – 34/48
= (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
= 14/3 – 13/4 + 13/6
The LCM (least common multiple) of the denominators 3, 4 and 6 is 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)
= 56/12 – 39/12 + 26/12
= (56 – 39 + 26)/12
= (82 – 39)/12
= 43/12
= 3⁷/₁₂
● Fraction
Representations of Fractions on a Number Line
Conversion of Mixed Fractions into Improper Fractions
Conversion of Improper Fractions into Mixed Fractions
Interesting Fact about Equivalent 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.
Recent Articles
-
Word Problems on Area and Perimeter | Free Worksheet with Answers
Jul 26, 24 04:58 PM
word problems on area and perimeter -
Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers
Jul 26, 24 04:37 PM
Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find… -
Perimeter and Area of Irregular Figures | Solved Example Problems
Jul 26, 24 02:20 PM
Here we will get the ideas how to solve the problems on finding the perimeter and area of irregular figures. The figure PQRSTU is a hexagon. PS is a diagonal and QY, RO, TX and UZ are the respective d… -
Perimeter and Area of Plane Figures | Definition of Perimeter and Area
Jul 26, 24 11:50 AM
A plane figure is made of line segments or arcs of curves in a plane. It is a closed figure if the figure begins and ends at the same point. We are familiar with plane figures like squares, rectangles… -
5th Grade Math Problems | Table of Contents | Worksheets |Free Answers
Jul 26, 24 01:35 AM
In 5th grade math problems you will get all types of examples on different topics along with the solutions. Keeping in mind the mental level of child in Grade 5, every efforts has been made to introdu…
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.