Question

The back wheel of a bicycle rotates 4 1/3 times with 1 2/9 rotations to pedal. Write the ratio of back wheel rotations to pedal rotations in simplest form

Answer 1

Data:

4 1/3 times with 1 2/9 wheel rotations to pedal

To write the ratio in simplest form you need to write mixed numbers as fractions:

4 1/3 is equal to 4 plus 1/3:

`4+(1)/(3)=(12+1)/(3)=(13)/(3)`

1 2/9 is equal to 1 plus 2/9:

`1+(2)/(9)=(9+2)/(9)=(11)/(9)`

You have the next ratio:

`(13)/(3)\colon(11)/(9)`

To simplify:

1. Find the least common denominator

LCD (13/3, 11/9)= 9

2. Rewrite the fractions with the least common denominator:

Multiply numerator and denominator of the fist fration by 3:

`\begin{gathered} (13\cdot3)/(3\cdot3)\colon(11)/(9) \\ \\ (39)/(9)\colon(11)/(9) \end{gathered}`

3. As the two fractions have the same denominator you multiply both fraction by the denominator:

`\begin{gathered} 9\cdot(39)/(9)\colon9\cdot(11)/(9) \\ \\ 39\colon11 \end{gathered}`Then, the ratio of back wheel rotations to pedal rotations in simplest form is 39:11