To add fractions with unlike denominators, you first find the least common denominator (LCD) and then convert the fractions to equivalent fractions with the LCD as the denominator. You then add the numerators and keep the LCD as the denominator of the final sum. For example, to add 2/5 + 1/3: find the LCD of 5 and 3 is 15; convert to equivalent fractions 6/15 + 5/15; add the numerators to get 11/15.

1. Adding Fractions With Unlike
Denominators
Fourth Grade Math
Mr. Mitchell

2. Adding Fractions with Unlike Denominators
• When adding fractions with unlike
denominators it is a little different than
fractions with like denominators.
• Unlike denominators means that the
denominators of the fractions are different.
2 1 1 2 3 1
3 5 6 9 12 6
The fractions above have different
denominators, called unlike denominators.

3. Adding Fractions with Unlike Denominators
• The goal of adding fractions with unlike
denominators is to get the denominators to be
the same.
• When the denominators are the same the
fraction is easier to add.
• As you have learned before, adding fractions
with like denominators are easier, because you
will just add the numerators.
• Our focus for this lesson is: To make our
denominators the same.

4. Adding Fractions with Unlike Denominators
• The following are the steps to adding fractions
with unlike denominators.
• Example:
2 1
5 3
As you can see, our fractions have unlike
denominators. To make them the same we
need to find the Least Common Denominator
or LCD.

5. Adding Fractions with Unlike Denominators
• To find our LCD we need to first find the
multiples of both of our denominators, and then
identify the Least Common Multiple, or LCM.
• The LCM will become our LCD.
• A multiple is the answer to a multiplication
problem.
 Example: multiples of 4 are: 4,8,12,16,20 and so
on.
 Multiples of 7 are: 7,14,21,28,35 and so on

6. Adding Fractions with Unlike Denominators
2 1
5 3
•Step 1
•Find the multiples of the
denominators, 5 and 3.
•Start with the lowest valued
number, because at times your
larger number may be a multiple of
your smaller number.
•Multiples of 3:
•3,6,9,12,15,18,21,24
•Multiples of 5:
•5,10,15
•Stop finding multiples when you have
found one they both have in common.

7. Adding Fractions with Unlike Denominators
2 1
5 3
•Step 2
•Identify the LCM
•The multiples are:
3: 3,6,9,12,15,18,24
5: 5,10,15
The Least Common Multiple is 15

8. Adding Fractions with Unlike Denominators
2 1
5 3
•Step 3
•Create equivalent fractions to your
current fractions, using your LCM as
your new denominator
2 ? 1 ?
5 15 3 15

9. Adding Fractions with Unlike Denominators
2 1
5 3
•To find an equivalent fraction, you will need to
find out what you multiplied each of the
original denominators by to get the new
denominator.
•First look at your multiples:
•3,6,9,12,15
•5,10,15
•You can count the number of multiples of
3 by counting how many multiples it takes
to get to 15
•Do the same for your multiples of 15

10. Adding Fractions with Unlike Denominators
2 1
5 3
•Step 3 continued:
•Remember, to find equivalent fractions,
whatever you do to the denominator you
must do the same to the numerator.
• For the fraction 2/5, you multiplied the
denominator by 3 so you need to multiply
the numerator by 3 as well.
•The equivalent fraction will
become:
2 6
5 15

11. Adding Fractions with Unlike Denominators
2 1
5 3
•Step 3 continued:
•Remember, to find equivalent fractions,
whatever you do to the denominator you
must do the same to the numerator.
• For the fraction 1/3, you multiplied the
denominator by 5 so you need to multiply
the numerator by 5 as well.
•The equivalent fraction will
become:
1 5
3 15

12. Adding Fractions with Unlike Denominators
2 1
5 3
•The fractions in the addition problem
then become:
6 5
15 15

13. Adding Fractions with Unlike Denominators
2 1
5 3
•Our goal was to convert our fractions
into fractions with the same
denominators. Following the steps you
have ended up with the following
fractions.
6 5
15 15

14. Adding Fractions with Unlike Denominators
2 1
5 3
Step 4
•Add the numerators of the fraction
together.
•6+5=11
•Eleven will be the numerator of
your answer.
6 5 11
15 15 ?

15. Adding Fractions with Unlike Denominators
2 1
5 3
Step 5
•The denominators are not added
together. The denominator tells us the
equal number of pieces all together so
this number does not change.
•Remember the following:
•If the denominators are the
same, keep them the same. If they
are not the same, make them the
same.
6 5 11
15 15 15

16. Adding Fractions with Unlike Denominators
2 1
5 3
6 5 11
15 15 15
The final step is to reduce the fraction if
needed. This fraction is already in the
simplest form, so reducing is not needed.

17. Adding Fractions with Unlike Denominators
• For further practice of adding fractions with
unlike denominators you can visit the following
websites:
 http://www.mathplayground.com/fractions_add.ht
ml
 http://www.aaamath.com/fra66kx2.htm
 http://www.math.com/school/subject1/practice/S
1U4L3/S1U4L3Pract.html
 Template for presentation provided by Microsoft
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