Question

Suppose a building inspector orders the height of a ceiling to be 8 feet tall, but the workers buy lumber that is only 50 centimeters tall. How many pieces of lumber will they have to stack to create an 8-foot ceiling? Explain your answer. (Hint: 1 inch = 2.54 centimeters.)

Answer 1

one way is change 50 cm to feet, then divide into 8 ft to get the number of 50 cm pieces needed:

To change units, use the idea of ratio of equal lengths, arranged so the units "cancel"
\[ 50 \cancel{\text{ cm } }\cdot \frac{1 \text{ in }}{1.54\cancel{\text{ cm}}}\cdot \frac{1 \text{ ft }}{12\text{ in}}= \text{ x ft} \]

now divide
\[ \frac{8 \text{ ft}}{x \text{ ft}} \]