Question

1. shawns golf club is 3\frac{3}{4} feet tall. shawns hockey stick is 5\frac{1}{2} feet tall.\

a how many times as tall as the golf club is the hockey stick? show your thinking.\
b what fraction of the hockey sticks height is the golf club? show your thinking.

Explanation:

Step1: Convert mixed numbers to improper fractions

Golf club height: \( 3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{15}{4} \) feet.
Hockey stick height: \( 5\frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2} \) feet.

Step2: Solve part (a) - How many times as tall

To find how many times the hockey stick is as tall as the golf club, divide hockey stick height by golf club height:
\( \frac{\frac{11}{2}}{\frac{15}{4}}=\frac{11}{2}\times\frac{4}{15}=\frac{44}{30}=\frac{22}{15}=1\frac{7}{15} \)

Step3: Solve part (b) - Fraction of hockey stick height

To find what fraction the golf club is of the hockey stick, divide golf club height by hockey stick height:
\( \frac{\frac{15}{4}}{\frac{11}{2}}=\frac{15}{4}\times\frac{2}{11}=\frac{30}{44}=\frac{15}{22} \)

Answer:

a. \( 1\frac{7}{15} \) times
b. \( \frac{15}{22} \)