Question

Juan learned that gear ratio refers to the number of times one gear rotates in relation to another gear. The ratio of the gears is 1 1/2 to 1/2Write two unit rates to represent the gear ratio

Answer 1

Let's define variables:
 x1: gear 1
 x2: gear 2
 The relationship between gears is:
 x1 / x2 = (1 1/2) / (1/2)
 Rewriting:
 x1 / x2 = (3/2) / (1/2)
 x1 / x2 = (3 * (1/2)) / (1/2)
 x1 / x2 = 3
 Another unit rate is:
 x2 / x1 = (1/2) / (1 1/2)
 x2 / x1 = (1/2) / (3/2)
 x2 / x1 = (1/2) / (3 * (1/2))
 x2 / x1 = 1/3
 Answer:
 two unit rates to represent the gear ratio are:
 x1 / x2 = 3
 x2 / x1 = 1/3