6.1.3 Equivalent Fractions
[ Why doesn’t this work with zero? You thought about that in Unit 2. ] If you multiply the numerator (the number on top) and the denominator (the number underneath) of any fraction by the same number (except zero), you will get a fraction that is equivalent to the original one:
Note: You must multiply the numerator and denominator by the same number because it is the same as multiplying by one, so it doesn’t change the value of the fraction.
You can also generate equivalent fractions by dividing the numerator (top number) and the denominator (bottom number) of the fraction by the same number (again, not zero).
Would you have reduced this fraction using different steps? This process of dividing the numerator (the number above the line) and the denominator (the value below the line) by the same number is known as “cancelling,” “reducing,” or “simplifying.” If there is no whole number that can be divided into both the numerator and the denominator, the fraction is said to be in lowest terms, or fully reduced. Answers are usually left in this form, as they are easier to visualize and understand (click on “View document”).