Question

current skill
lee climbed one third of a mountain in one ninth of a month. find the rate in mountains per month.
label optional
123 abc
0 1 2 3 4 + - * ÷
5 6 7 8 9 = . , $
x y π < ≤ > ≥ % !
skill code: 222003

Explanation:

Step1: Recall rate formula

Rate is defined as the amount of work done divided by the time taken. Here, the work is the fraction of the mountain climbed, and the time is the fraction of the month. So, rate \( r=\frac{\text{Amount of mountain climbed}}{\text{Time taken}} \).

Step2: Substitute values

The amount of mountain climbed is \( \frac{1}{3} \) and the time taken is \( \frac{1}{9} \) of a month. So, \( r = \frac{\frac{1}{3}}{\frac{1}{9}} \).

Step3: Divide fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So, \( \frac{\frac{1}{3}}{\frac{1}{9}}=\frac{1}{3}\times\frac{9}{1} \).

Step4: Simplify the multiplication

\( \frac{1\times9}{3\times1}=\frac{9}{3} = 3 \).

Answer:

\( 3 \)