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:

Part (a)

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: Divide hockey stick height by golf club height

To find how many times taller the hockey stick is, calculate \( \frac{11}{2}\div\frac{15}{4} \).
Dividing fractions: \( \frac{11}{2}\times\frac{4}{15}=\frac{11\times4}{2\times15}=\frac{44}{30}=\frac{22}{15}=1\frac{7}{15} \).

Part (b)

Step1: Use the same improper fractions as before

Golf club: \( \frac{15}{4} \), Hockey stick: \( \frac{11}{2} \).

Step2: Divide golf club height by hockey stick height

Calculate \( \frac{15}{4}\div\frac{11}{2} \).
Dividing fractions: \( \frac{15}{4}\times\frac{2}{11}=\frac{15\times2}{4\times11}=\frac{30}{44}=\frac{15}{22} \).

Final Answers:

(a)

Answer:

\( 1\frac{7}{15} \) (or \( \frac{22}{15} \))

(b)