Exercise 36 Page 120

We are given the quantity 9 yards and shown a series of steps to convert it into feet. We are asked to find where the mistake was made. Let's start by analyzing the first step. 9 yd = ? ft ✓ The previous statement just says that the 9yards will be converted to feet. There is no error at this point. Let's see the next step. 9 yd * 3 yd/1 ft &= 27 ft *Notice that the conversion factor used implies an incorrect equivalence. In truth, 1yard is equal to 3feet. 3 yd & ≠ 1 ft 1 yd &= 3 ft Furthermore, the multiplication is done incorrectly. Had they multiplied correctly, the calculation would be 27 yd^2ft. 9 yd * 3 yd/1 ft = 27 yd^2/ft Although this result is also incorrect, we immediately realize that the resulting units are not given in feet. To find the correct answer, we need to use the correct conversion factor. We need to have 1yard in the denominator in our conversion factor so that the yards cancel out. 1 yd = 3 ft_(⇓) 3 ft/1 yd The correct procedure for the conversion is shown below. 9 yd &= ? ft [0.3em] 9 yd * 3 ft/1 yd &= 27 ft Hence, 9 yards are equivalent to 27 feet.