# 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.

- Overview
- Number Types
- Factors
**Fractions**- Structure
- Reducing
- More or Less
- Mixed Numbers
- Mixed Numbers 2
- Addition
**Subtraction 1**- Subtraction 2
- Multiplication
- Division
- Word Problems
- Real World
- Decimals
- Percentages
- Estimation
- Ratios
- Money
- Activities
- More Maths Topics

# Useful Reference Materials

**Wikipedia:**

*https://en.wikipedia.org/wiki/Fraction_%28mathematics%29*

**Encyclopædia Britannica:**

*http://www.britannica.com/topic/fraction*

**University of Delaware:**

*https://sites.google.com/a/udel.edu/fractions/*