Adding Two Fractions with Different Denominators :
In this section, we will learn, how to add fractions with different denominators.
We can use one of the following methods to add two fractions with different denominators.
If the denominators of the fractions are co-prime or relatively prime, we have to apply this method.
Fro example, let us consider the two fractions 1/8, 1/3.
In the above two fractions, denominators are 8 and 3.
For 8 and 3, there is no common divisor other than 1.
So 8 and 3 are co-prime.
Here we have to apply cross-multiplication method to add the two fractions 1/8 and 1/3 as given below.
If the denominators of the fractions are not co-prime (there is a common divisor other than 1), we have to apply this method.
Fro example, let us consider the two fractions 5/12, 1/20.
In the above two fractions, denominators are 12 and 20.
For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.
For 12 & 20, we have the following common divisors other than 1.
2 and 4
So 12 and 20 are not co-prime.
In the next step, we have to find the LCM (Least common multiple) of 12 and 20.
To find the LCM of 12 and 20, divide both 12 and 20 by the greatest common divisor as shown below.
The greatest common divisor of 12 and 20 is 4.
LCM is the product of the divisors and undivided numbers.
Therefore, LCM of 12 and 20 is
= 4 ⋅ 3 ⋅ 5
= 60
Now, make the denominators of both the fractions as 60 using multiplication and then add them.
Problem 1 :
Add :
1/12 + 1/16
Solution :
The given two fractions are unlike fractions. Because, they have different denominators.
For 12 and 16, we have the following common divisors other than 1.
2 and 4
So 12 and 16 are not co-prime.
In the next step, we have to find the LCM (Least common multiple) of 12 and 16.
LCM of (12 and 16) = 48
Now, make the denominators of both the fractions as 48.
To make the denominator of both the fractions as 48 , we have to multiply the numerator and denominator of the first fraction by 4 and the second one by 3.
Then, we have
1/12 + 1/16 = 4/48 + 3/48
1/12 + 1/16 = (4 + 3) / 48
1/12 + 1/16 = 7 / 48
So, the sum of the two fractions is 7/48.
Problem 2 :
Add :
3/20 + 7/30
Solution :
The given two fractions are unlike fractions. Because, they have different denominators.
For 20 and 30, we have the following common divisors other than 1.
2, 5 and 10
So 20 and 30 are not co-prime.
In the next step, we have to find the LCM (Least common multiple) of 20 and 30.
LCM of (20 and 30) = 60
Now we have to make the denominators of both the fractions as 60.
To make the denominator of both the fractions as 60, we have to multiply the numerator and denominator of the first fraction by 3 and and for the second fraction by 2.
Then, we have
3/20 + 7/30 = 9/60 + 14/60
3/20 + 7/30 = (9 + 14) / 60
3/20 + 7/30 = 23 / 60
So, the sum of the two fractions is 23/60.
Problem 3 :
Add :
3/7 + 2/9
Solution :
The given two fractions are unlike fractions. Because, they have different denominators.
For 7 and 9, there is no common divisor other than 1.
So 7 and 9 are co-prime
Here, we have to apply cross multiplication method to add the two fractions.
To add the two fractions, we have to do the following three steps.
Step 1 :
Multiply the numerator of the first fraction by denominator of the second fraction.
Step 2 :
Multiply the numerator of the second fraction by denominator of the first fraction.
Step 3 :
Multiply the denominators of the two fractions.
When we do the above three steps, we will have
3/7 + 2/9 = (27 + 14) / 63
3/7 + 2/9 = 41 / 63
So, the sum of the two fractions is 41 / 63.
After having gone through the stuff and examples, we hope that the students would have understood, how to add two fractions with different denominators.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
May 22, 22 03:05 AM
Linear Growth and Decay
May 22, 22 01:15 AM
Worksheet on Probability
May 22, 22 01:12 AM
Probability Worksheet