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Some fractions that at first glance appear to be different from one another are really the same. For instance, suppose that we cut a pizza into 8 equal slices,
and then eat 4 of the slices. The shaded portion of the diagram
at the right represents the amount eaten. Do you see in this
diagram that the fractions We say that these fractions are equivalent . Any fraction has infinitely many equivalent fractions. To see
why, lets consider the fraction All the shaded portions of the diagrams are identical, so A faster way to generate fractions equivalent to So Can you explain how you would generate fractions equivalent to
To Find an Equivalent Fraction for
Explain why neither b nor n can be equal to 0 here. An important property of equivalent fractions is that their cross products are always equal. In this case, EXAMPLE 1 Find two fractions equivalent to Solution Lets multiply the numerator and denominator by 2 and then by 6. We use cross products to check. So So EXAMPLE 8 Write Solution The question is:
Therefore Both 3 · 35 and 7 · 15 equal 105. |