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
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