This is the second page on subtracting fractions. If you want to see some simpler examples with like and unlike fractions, just click here. If not, let's look at mixed numbers.

# Subtracting Mixed Numbers

You've got fractions with**common denominators**and unlike fractions under control now. Let's look at an example with

**mixed numbers**before we go. Our first example will look at mixed numbers that have common denominators.

**4 3/9 - 2 2/9 = ?**

• Check for common denominators: They are like fractions with a common denominator of 9. Do nothing.

• Subtract the numerators from each fraction: 3 - 2 = 1

• Write the difference of the numerators above the common denominator: 1/9

• Subtract the whole numbers: 4 - 2 = 2

• Write out the new mixed number: 2 1/9

• Simplify: 1/9 can't be simplified. You are done.

Answer: 4 3/9 - 2 2/9 = 2 1/9

What happens if you have unlike fractions in the mixed numbers? You'll have to create that pesky common denominator to finish the problem. Let's try this example:

**5 7/8 - 3 3/4 = ?**

• Common denominators: We've got 4 and 8. They have a common factor of four, so we only need to fix the 3/4 fraction.

3/4 = 3/4 * 1 = 3/4 * 2/2 = (3*2)/(4*2) = 6/8

You can now rewrite the problem as 5 7/8 - 3 6/8 = ?

• Subtract the numerators from each fraction: 7 - 6 = 1

• Write the difference of the numerators above the common denominator: 1/8

• Subtract the whole numbers: 5 - 3 = 2

• New mixed number: 2 1/8

• Simplify: 1/8 is already simplified, so you are good.

Answer: 5 7/8 - 3 3/4 = 2 1/8

One last example before we let you go. You may find a situation where you need to subtract fractions, but the amounts will require you to

**borrow**or

**regroup**numbers like you do in regular subtraction. Think about 22 - 8. You would need to borrow from the tens column to finish the problem. The same thing can happen with fractions. You're going to need to borrow from the whole number in the mixed number. 1 1/8 - 3/8 is a good example. You have plenty to work with, but subtracting 3/8 from 1/8 is going to cause you a problem. There are several ways to solve these problems. We're going to offer one example here. No issues with common denominators for this one.

**6 1/8 - 2 5/8 = ?**

• Common denominators: We're good with 8.

• Make improper fractions: Usually you can just subtract here and move forward, but 1-5 is going to give you a -4 for an answer. You could just subtract and get that negative number as a result, but we're going to use

**improper fractions**to solve the problem. Remember how to make improper fractions? The numerator will be larger than the denominator. Start by turning the whole number into a fraction and then add the two parts to make an improper fraction.

6 1/8 = 6 + 1/8 = 6/1 + 1/8 = 48/8 + 1/8 = 49/8

2 5/8 = 2 + 5/8 = 2/1 + 5/8 = 16/8 + 5/8 = 21/8

• Replace your mixed numbers with improper fractions in the original problem: 49/8 - 21/8 = ?

• Subtract the numerators: 49 - 21 = 28

• Write the difference of the numerators above the common denominator: 28/8

• Convert the improper fraction to a mixed number: Remember this is just a division problem with a remainder: 28 ÷ 8 = 3r4 = 3 4/8

• Simplify the mixed number: We have a 4/8. To simplify, we will use the common factor 4. Divide the numerator and denominator by 4 and you will get 1/2.

Answer: 6 1/8 - 2 5/8 = 3 1/2

It takes a little bit longer, but when you get stuck, converting mixed numbers to improper fractions is super useful. You can use it all the time when you multiply and divide fractions.

# Negative Values

You may get problems where you subtract a larger fraction from a smaller one. Your answer will wind up less than zero. It's just like regular subtraction. Remember that 1 - 4 = -3. Let's do a fraction with those numbers...**1/5 - 4/5 =?**

• Common denominators: Yes.

• Subtract the numerators: 1 - 4 = -3

• Write the difference of the numerators above the common denominator: -3/5

• Simplify: -3/5 cannot be simplified. You're done!

Answer: 1/5 - 4/5 = -3/5

We'll get into subtracting mixed numbers when we do an algebra review, but you can figure it out from these tools. We think the easiest way is to use improper fractions. Here's a quick example with no explanation. You can see what we did:

**2 3/8 - 4 5/8 = ?**

• Convert to improper:

2 3/8 = 2 + 3/8 = 16/8 + 3/8 = 19/8

4 5/8 = 4 + 5/8 = 32/8 + 5/8 = 37/8

• Substitute: 19/8 - 37/8 = ?

• Subtract numerators: 19 - 37 = -18

• Answer as improper: -18/8

• Convert to mixed: -18/8 = -18 ÷ 8 = -2r2 = -2 2/8

• Simplify: 2/8 has the common factor 2, so the simplified form is 1/4.

Final Answer: 2 3/8 - 4 5/8 = -2 1/4

Let's move on to fraction multiplication now. It's going to be really easy when you compare it to all the common denominator work we do with addition and subtraction.

- 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/*