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:

$4+\frac{1}{3}=\frac{12+1}{3}=\frac{13}{3}$

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

$1+\frac{2}{9}=\frac{9+2}{9}=\frac{11}{9}$

You have the next ratio:

$\frac{13}{3}\colon\frac{11}{9}$

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:

$\begin{gathered} \frac{13\cdot3}{3\cdot3}\colon\frac{11}{9} \\ \\ \frac{39}{9}\colon\frac{11}{9} \end{gathered}$

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

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