Adding Fractions with Unlike Denominators

Adding Fractions With Unlike Denominators

Fourth Grade MathMr. Mitchell

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.

5

1

3

2

The fractions above have different denominators, called unlike denominators.

9

2

6

1

6

1

12

3


• 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.


• The following are the steps to adding fractions with unlike denominators.

• Example:

3

1

5

2

As you can see, our fractions have unlike denominators. To make them the same we need to find the Least Common Denominator or LCD.


• 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


3

1

5

2

• 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.


3

1

5

2

• 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


3

1

5

2

• Step 3• Create equivalent fractions to your

current fractions, using your LCM as your new denominator

15

?

5

2

15

?

3

1


3

1

5

2

• 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


3

1

5

2

• 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:

15

6

5

2


3

1

5

2

• 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:

15

5

3

1


3

1

5

2

• The fractions in the addition problem then become:

15

5

15

6


3

1

5

2

• Our goal was to convert our fractions into fractions with the same denominators. Following the steps you have ended up with the following fractions.

15

5

15

6


3

1

5

2

Step 4• Add the numerators of the fraction

together. • 6+5=11

• Eleven will be the numerator of your answer.

?

11

15

5

15

6


3

1

5

2

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.

15

11

15

5

15

6


3

1

5

2

15

11

15

5

15

6

The final step is to reduce the fraction if needed. This fraction is already in the simplest form, so reducing is not needed.


• For further practice of adding fractions with unlike denominators you can visit the following websites: http://

www.mathplayground.com/fractions_add.html http://www.aaamath.com/fra66kx2.htm http://

www.math.com/school/subject1/practice/S1U4L3/S1U4L3Pract.html

Template for presentation provided by Microsoft PowerPoint 07

http://www.mathplayground.com/fractions_add.html

http://www.mathplayground.com/fractions_add.html

http://www.aaamath.com/fra66kx2.htm

http://www.aaamath.com/fra66kx2.htm

http://www.math.com/school/subject1/practice/S1U4L3/S1U4L3Pract.html



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Adding Fractions with Unlike Denominators