How to Add Unlike Fractions

Have Multiplication Facts Memorized

Is your child struggling to add or to subtract unlike fractions? What are unlike fractions? They are fractions with different denominators.  First, I can not re-emphasize how important it is for the child to have his multiplication facts memorized!

Multiplication facts MUST be memorized for your child to truly be successful in math.

steps to add unlike fractions

how to add unlike fractions

Be Able to find the Least Common Multiple

Next, your child needs to know how to find the Least Common Multiple (LCM) of numbers.  Many students confuse LCM and the Greatest Common Factor (GCF).  My trick to remember is the M in LCM reminds me to think of my multiplication facts.

So to find LCM(3,4), we think of our multiplication facts for each number:

Positive Multiples of 3:  3, 6, 9, 12, 15 ,…..

Positive Multiples of 4:  4, 8, 12, 16, …..

So the LCM(3,4) = 12 as that’s the first positive multiple 3 and 4 have in common.

Be Able to Add Like Fractions

Then because we are changing unlike fractions to like fractions (fractions with the same denominator), students have to be able to add like fractions.

With like fractions, you simply add the numerator and keep the same denominator.

Example of Adding Unlike Fractions

Suppose we want to do 1/2 + 1/3.

Step 1:  First, we find the LCM.  Again, the LCM is the first multiplication fact the numbers 2 and 3 have in common.

Positive multiples of 2:  2, 4, 6, 8, 10, …

Positive multiples of 3:  3, 6, 9, 12, ….

So LCM(2,3) = 6

Step 2:  So we want the denominator of both of our fractions to be 6.  We need to multiply the 2 in 1/2 by 3 to change it to a 6, so we MUST ALSO MULTIPLY the 1 in 1/2 by 3 as well, so that in total, we are multiplying 1/2 by 3/3 (which is equal to 1).  When we multiply 1/2 by 3/3, we are creating an equivalent fraction, 3/6.

To change the 3  in 1/3 to a 6, we multiply the 3 by a 2, so we must also multiply the 1 in 1/3 by a 2 as well, so that in total, we are multiplying 1/3 by 2/2 (which is equal to 1).  When we multiply 1/3 by 2/2, we create the equivalent fraction 2/6.

Step 3:  We end up with 3/6 + 2/6.  Now we have two like fractions (because they have the same denominator).  To add two like fractions we simply add the numerators, and keep the denominator. 

Just think if you ate 3/6 of a pizza, and then ate 2/6 of a pizza, in total you ate 5/6 of  pizza.

It’s very important that your child be able to add unlike fractions to excel in math.

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