Equivalent Fractions

When two fractions represent the same value, we call them equivalent fractions. There are infinitely many ways to represent a fractional value.

EXAMPLE:     1/4 = 2/8 = 3/12 = 4/16 = 5/20 = 6/24 = 7/28 = 8/32 = .......

To find an equivalent fraction, we use the Fundamental Law of Fractions, which states that the value of the fraction does not change when the numerator and denominator are multiplied by the same non-zero number.

EXAMPLE:  3 * 8 = 24
 3 * 9    27

   We can apply the Fundamental Law of Fractions backwards to simplify fractions. We do this by dividing numerator and denominator by the same common factor.

EXAMPLE:  12 -:- 4 = 3
 16 -:- 4    4

     Notice that when we multiply or divide both the numerator and denominator by the same number, we are in effect multiplying or dividing the fraction by one (4/4 = 1) and so we are not changing the value of the fraction, only the way that value is being represented. Fractions where the numerator and denominator do not have a common divisor are said to be in simplest form. Note: we avoid the term reduced form because this term suggests that the fraction in simplest form is smaller than the unsimplified fraction.

MOVIE: Fraction track video #1

PRACTICE: Fresh-Baked Fractions
Cuisenaire fractions applet

After Equivalent Fractions:
Ordering fractions
Denseness property