 # 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.

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