Question

What property of multiplication allows you to multiply a rate by a conversion factor without changing its value?

Answer 1

A conversion factor originally known as unity bracket method, is a mathematical tool for converting between units of measurement. It is sometimes referred to as a unit multiplier, and consists of a fraction in which the denominator is equal to the numerator. A conversion factor is used to change the units of a measured quantity without changing its value. Because of the identity property of multiplication, the value of a number will not change as long as it is multiplied by one.Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity. For example, Days are converted to hours, by multiplying the days by the conversion factor as 24. The conversion can be reversed by dividing, the hours, by 24 to get days; however, the reciprocal 1/24 could be considered the reverse conversion factor for an hours-to-days conversion, where 1/24 ~= 0.0416666666667. Hence, the term "conversion factor" is the multiplier which yields the result, not a divisor from that viewpoint. To yield hours, the conversion factor is 24, not 1/24, so: hours = days × 24 (multiplying by the factor). Examples of Conversion Factors Since 1 day = 24 hours = 1440 minutes, therefore 15 minutes (1 day/1440 minutes) = 15/1440 ~= 0.010416667 = ~0.01 days. Since 1 hour = 60 mins = 3600 seconds, therefore 7200 seconds = 120 mins = 2 hours.