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Adding and Subtracting Unlike Fractions

Adding (or subtracting) unlike fractions is more complicated than adding (or subtracting) like fractions. An extra step is required: changing the unlike fractions to equivalent like fractions. For instance, suppose that we want to add . Even though we can use any common denominator for these fractions, let’s use their least common denominator to find equivalent fractions.

10 = 2 · 5

15 = 3 · 5

LCD = 2 · 3 · 5 = 30

Let’s rewrite the fractions vertically as equivalent fractions with the denominator 30.

Now we add the equivalent like fractions.

So .

We can also add and subtract unlike fractions horizontally.

To Add (or Subtract) Unlike Fractions

  • rewrite the fractions as equivalent fractions with a common denominator, usually the LCD;
  • add (or subtract) the numerators, keeping the same denominator; and
  • write the answer in simplest form.




First, we find the LCD, which is 48. After finding equivalent fractions, we add the numerators, keeping the same denominator.


Subtract .


Because 3 is a factor of 12, the LCD is 12. Again, let’s set up the problem vertically.


Combine: .


We add and then subtract from this sum. The LCD of is 6.

Next, we subtract . Their LCD is 10.


Do you see another way of solving this problem, using the LCD of all three fractions?


Find the perimeter of the figure.


Recall that the perimeter of a figure is the sum of the lengths of its sides.

The perimeter of the figure is feet.

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