Equivalent Ratios

Students learn to find equal ratios by first writing the given ratio as a fraction, then multiplying the numerator and denominator of the fraction by the same number. For example, to find two ratios that are equal to 1:7, first write 1:7 as the fraction 1/7. Next, multiply both the numerator and denominator of 1/7 by 2, to get 2/14, or 2:14, and multiply the numerator and denominator of 1/7 by 3, to get 3/21, or 3:21. So 2:14 and 3:21 are two ratios that are equal to 1:7. Students are also asked to determine whether two given ratios are equal, by first writing each ratio as a fraction, then writing each fraction in lowest terms. If the two fractions are the same when written in lowest terms, then the ratios are equal.