# Reducing Fractions

To solve problems in your classes you will have to create larger**equivalent fractions**and smaller

**reduced fractions**. Many of your answers will come out as fractions such as 4/8 or 12/15. Your teachers will want those fractions reduced into their simplest forms. A reduced fraction is an equivalent fraction. They will have the same value even though the numbers are different.

You will need to find

**common factors**that can divide into both the

**numerator**and

**denominator**of the fraction. When there are no common factors in the numerator and denominator, you have a fraction that has been reduced to its simplest form.

**Example:**4/8

• Both of the vales are even, so your first step will be to divide both the top and bottom numbers by 2.

• Now you have 2/4. It's still not good enough. Let's divide by 2 one more time.

• Now you have 1/2. That fraction can't be reduced any further. Your teacher will want that answer.

• Now you also know that 1/2 and 4/8 are equivalent fractions.

**Example:**12/15

• For this example, 2 won't work, since 15 is odd. Factors of 12 include 2, 3, 4, and 6. Factors of 15 include 3 and 5. Both the numerator and denominator are divisible by 3. Let's try that.

• Now you have 4/5. This fraction was reduced with only one try. 4/5 is the simplest form.

• Now you also know that 4/5 and 12/15 are equivalent fractions.

**Example:**16/48

• Let's look at factors for each number. Factors of 16: 1, 2, 4, 8, 16. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

• Notice that both values have a factor of 16. Let's divide the top and bottom numbers by 16.

• Your new fraction is 1/3. It is the simplest form of the fraction. That was fast.

• Now you also know that 1/3 and 16/48 are equivalent fractions.

When you are reducing fractions, look for prime numbers in the numerator or denominator. In many fraction problems, they will reduce to a prime number in the numerator or denominator. It doesn't always work, but it is a giveaway that you are done. In the above examples, the denominators were 2, 5 and 3. All of those are prime numbers.

# Before We Go...

**• Is 1/2 the reduced form of 3/4? No.**Three fourths cannot be simplified. 3 and four have no common factors.

**• Can 6/8 be simplified to 3/4? Yes.**6 and 8 have the common factor 2. When you divide, 6÷2=3 and 8÷2=4.

**• Are 4/6 and 20/30 equivalent fractions? Yes.**20 and 30 have the common factor 5. When you divide, 20÷5=4 and 30÷5=6. You can reduce 20/30 to 4/6 so they are equivalent. The simplest form of both fractions is 2/3.

- 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/*