4.3+Equivalent+Fractions

Section 4.3 - Equivalent Fractions

 * Equivalent Fractions - Fractions that have the same value, even if they don't look the same. **

There are two main ways to create equivalent fractions: A. Reduce B. Build Up

Anything times 1 equals itself. Anything divided by 1 equals itself. Also, a number divided by itself equals 1.



__To create equivalent fractions by reducing__, find a factor that goes into both the numerator and denominator evenly. Divide that factor from both the numerator and denominator. Using the example above, if you started with 6/15 and "divided out" a 3 on top and bottom, you would reduce it to 2/5, which is an equivalent fraction.


 * Reducing to Lowest Terms ** means that you have reduced the fraction using this method until there are no more common factors between the numerator and denominator except 1. This is a very important process. Unless told otherwise, always reduce fractions to lowest terms to complete a math problem.


 * Simplifying Fractions ** - means the same as reducing to lowest terms.

__To create equivalent fractions by building up__, multiply the numerator and denominator by the same number. In the above example, we started with 2/5 and multiplied both top and bottom by 3, to get the equivalent fraction of 6/15.

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 * It's usually the denominator that matters.**

You will learn later in this chapter why the denominator often determines what number you will multiply, or divide, both the numerator and denominator by.

Suppose you have 5/6 and you want to find an equivalent fraction with a denominator of 24. You will need to figure out what number to multiply the first denominator by, in order to get the second denominator. You will multiply both the numerator and denominator by the same number in order to find an equivalent fraction.

The mystery factor is 4, because you would have to multiply 6 times 4 to get 24. So, you would multiply both numerator and denominator by 4 and find that 20 over 24 is equivalent to 5/6.

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 * Chapter Four Practice Problems**

**Where to from here?**
4.1 Greatest Common Factor 4.2 What is a Fraction? 4.3 Equivalent Fractions 4.4 Multiplying Fractions 4.5 Dividing Fractions 4.6 Adding and Subtracting Like Fractions 4.7 Adding and Subtracting Unlike Fractions 4.8 Fraction Coefficients 4.9 Solving for X with Fractions Chapter Four Review Chapter Four Homework