A plumber drilled a hole in a wall such that its diameter is slightly larger than three thirty-seconds inch. Determine which of the following is the smallest measure that is still larger than three over 32 inches.
To solve this problem, we need to be able to order these fractions. And to order all of these fractions, we want them to have a common denominator. We’re comparing three over 32 to one-fourth, five sixteenths, five sixty-fourths, thirteen thirty-seconds, and twenty-five sixty-fourths.
I notice that 64 is equal to 32 times two. And 64 can be divided by four and 16. We can use 64 as our common denominator. Five sixty-fourths stays the same. Twenty-five sixty-fourths stays the same. To get from 32 to 64, we multiplied the denominator by two. And if we multiplied the denominator by two, we also must multiply the numerator by two. Three times two is six. We do the same thing with thirteen thirty-seconds. 32 times two equals 64. 13 times two equals 26. From there, we know that 16 times four equals 64. And five times four equals 20. Four times 16 equals 64. And one times 16 equals 16.
We are looking for the smallest measure that is still larger than three over 32. Which of these five fractions is the smallest measure that’s still bigger than six over 64? Five over 64 is not larger than six over 64. Because we have a common denominator, the smallest measure will be the fraction with the smallest numerator.
Out of the four remaining choices, 16 over 64 is the smallest measure that’s still larger than six over 64. And 16 over 64 is equal to one-fourth of an inch, which is answer choice a.