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
-
Conversion of Rupees and Paise | How to convert rupees into paise?
Feb 12, 25 02:45 AM
We will discuss about the conversion of rupees and paise (i.e. from rupees into paise and from paise into rupees). How to convert rupees into paise? First we need to remove the point and then remove -
Writing Money in Words and Figure Worksheet With Answers | All Grades
Feb 12, 25 02:30 AM
In writing money in words and figure worksheet we will get different types of questions on expressing money in words and figures, write the amount in short form (in figures) and write the amount in lo… -
Writing Money in Words and Figure | Rules for Writing Money in Words
Feb 12, 25 01:59 AM
Rules for writing money in words and figure: 1. Abbreviation used for a rupee is Re. and for 1-rupee it is Re. 1 2. Rupees is written in short, as Rs., as 5-rupees is written as Rs. 5 -
Worksheet on Money | Conversion of Money from Rupees to Paisa
Feb 11, 25 09:39 AM
Practice the questions given in the worksheet on money. This sheet provides different types of questions where students need to express the amount of money in short form and long form -
Worksheet on Measurement | Problems on Measurement | Homework |Answers
Feb 10, 25 11:56 PM
In worksheet on measurement we will solve different types of questions on measurement of length, conversion of length, addition and subtraction of length, word problems on addition of length, word pro…
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.