Quoto

Learn / Library / Mental math

Bracketing a quotient

Mental mathHard

A trader bounds so that the range is certain to contain the value. The numerator may be rounded only to an adjacent multiple of , either down or up, and the denominator only to an adjacent multiple of , either down or up; for each end, the directions are chosen to make the low end as low as possible and the high end as high as possible. What is the ratio of the high end to the low end? Give a fraction in lowest terms.

Checking an answer needs JavaScript. The hint and the solution open without it.

A whole number, a decimal, a fraction like 3/8 or a percent.

Hint

A quotient grows when the top grows and when the bottom shrinks.

Solution
  1. The quotient is smallest with a small top and a big bottom, so the low end is .
  2. It is largest with a big top and a small bottom, so the high end is .
  3. As a check, lies inside the range.
  4. The ratio is .

Answer:

Back to the library