Adding and Subtracting Fractions with Unlike Denominators

This week we will be discussing how to add and subtract fractions with different denominators (bottom numbers).

Let's start with adding fractions with unlike denominators.

In order to solve this type of problem, we need to find the least common multiple of the denominators. Once we figured out the least common multiple, we need to multiply the denominator (the bottom number) and numerator (the top number) by the same value that was used to get the least common multiple.

Example:

The least common multiple between my denominators 6 and 4 is 24.

I can find that by making a list of each numbers multiples or by finding the prime factors of 6 and 4.

Now I ask myself, "Self, what is the number that I multiplied 6 by in order to get 24?" Yep! "I multiplied 4 times 6 to get 24." So that means I must also multiply 4 by 5, my numerator (my top number) in order to get an equal fraction. So 4 times 5 is 20, and 4 times 6 is 24. My new fraction is 20/24.

Now I follow the same steps with the other fraction.

4 times 6 is 24. So 3 times 6 is 18. My new fraction is 18/24

Now I just add the numerators and put my answer over my denominator 24.

20 + 18= 38

Now, I place 38 over my denominator 24. 

My answer is   38  .

                        24

I can simplify 38 twenty-fourths, by dividing 38 by 24 to get a mixed number. 24 goes into 38 one time, so 1 is my whole number in front of my new fraction. I take the remainder 14 and place it over the denominator 24.

My simplified answer looks like this.

If you are a visual learner, and you need to see how the fractions are equal with a common denominator, then you can use the fraction strip picture below. Feel free to print and cut the picture below. You may need to print a few copies to get to the right numerator.

Fraction Strips