 # Basic Steps of Subtracting Fractions

Hopefully, you just looked at the page on adding fractions. The rules for subtracting fractions are almost the same. You'll be looking for those common denominators. There is a risk with subtraction that you'll get some negative numbers, and we'll give you an example for that possibility too. Don't worry. It's just like regular subtraction.

# Subtracting Fractions with the Same Denominators

We'll start with simple examples and give you some fractions with the same denominators (number on the bottom). Subtracting like fractions is similar to regular subtraction. You only need to focus on the numerators (numbers on top).

6/13 - 1/13 = ?
• Create common denominators: They are already the same at 13, so we do nothing.
Subtract the second numerator from the first: 6 - 1 = 5
Write the difference of the numerators above the common denominator: 5/13.
Simplify the fraction if you need to. 5/13 cannot be simplified. You are done.
Answer: 6/13 - 1/13 = 5/13

7/9 - 1/9 = ?
• Create common denominators: The denominators are the same. Do nothing.
• Subtraction of numerators: 7 - 1 = 6
• Write the difference of the numerators above the common denominator: 6/9.
• Simplify: 6 and 9 have a common factor of 3. When you divide the numerator and denominator by 3 you get 2/3.
Answer: 7/9 - 1/9 = 6/9 = 2/3

# Creating Common Denominators

Let's get more advanced. What about subtracting unlike fractions? You don't have common denominators. We've looked at creating equivalent fractions in an earlier lesson. You will use that process here.

1/3 - 1/7 = ?
• Create common denominators: We have 7 and 3. They have no common factors, so let's just multiply to create two new equivalent fractions. Remember how we multiplied by equivalents of 1? It went like this...
1/3 = 1/3 * 1 = 1/3 * 7/7 = (1*7)/(3*7) = 7/21
1/7 = 1/7 * 1 = 1/7 * 3/3 = (1*3)/(7*3) = 3/21
You now have the common denominator 21.
• Rewrite the problem as 7/21 - 3/21 = ?
• Subtract numerators: 7 - 3 = 4
• Write the difference of the numerators above the common denominator: 4/21
• Simplify: 4/21 cannot be simplified. You are done.
Answer: 1/3 - 1/7 = 4/21

Let's try one more with unlike fractions.

4/5 - 2/3 = ?
• Create common denominators: We have 5 and 3. They have no common factors, so let's just multiply by equivalents of 1 to create two new equivalent fractions:
4/5 = 4/5 * 1 = 4/5 * 3/3 = (4*3)/(5*3) = 12/15
2/3 = 2/3 * 1 = 2/3 * 5/5 = (2*5)/(3*5) = 10/15
You now have the common denominator 15.
• Rewrite the problem as 12/15 - 10/15 = ?
• Subtract numerators: 12 - 10 = 2
• Write the difference of the numerators above the common denominator: 2/15
• Simplify: 2/15 cannot be simplified. You are done.
Answer: 4/5 - 2/3 = 2/15

You will find more problems like this in your homework. We also have a second page on subtracting fractions where we talk about negative values and mixed numbers.

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