Last night, the temperature fell from 0°F to Negative 13 and one-fifth°F in4 and two-fifths hours. Alan calculated the average temperature change per hour. Negative 13 and one-fifth divided by 4 and two-fifths = Negative StartFraction 66 over 5 EndFraction divided by StartFraction 22 over 5 EndFraction = Negative StartFraction 66 over 5 EndFraction (StartFraction 22 over 5 EndFraction) = Negative StartFraction 1,452 over 25 EndFraction Alan solved the problem, but when he checked the answer by estimating, it didn’t seem right. What error did he make?

It is written in the form p/q, read as "p by q", where p is called the numerator and q is called the denominator, and the fraction p/q represents p number of equal parts from q number of equal parts.

Fractions are of two types:

Proper fraction: Where numerator < denominator.
Improper fraction: Where numerator > denominator. These fractions are written in mixed form also.

How are fractions divided?

Fractions are divided by multiplying the dividend by the reciprocal of the divisor

Suppose we are asked to divide a fraction a/b by x/y.

This is written as (a/b) ÷ (x/y) or (a/b)/(x/y), and calculated as:

(a/b)*(y/x).

How to solve the question?

In the question, we are informed that last night, the temperature fell from 0°F to Negative 13 and one-fifth °F in 4 and two-fifths hours. Alan calculated the average temperature change per hour.

He followed the following steps:

-(13 1/5)/(4 2/5)

= -(66/5)/(22/5)

= -(66/5)(22/5)

= -(1452/25).

The mistake lies in step -(66/5)/(22/5) → -(66/5)(22/5) where he didn't take the reciprocal of the divisor while dividing the two fractions.