Question

Nathaniel measured the height of one shelf on his bookcase. He wants to know which books will fit on the shelf. The shelf is 22.86 sentimeters tall. He measured it again with an inch ruler. The shelf is 9 inches tall.
PART A - Wrte an equatioon you could use to find the number of centimeters in 1 inch.

PART B - Solve the equation you wrote in PART A. Show your work.

PART C - The top shelf of Natheniel's bookcase is 12 inches tall. How many centimeters tall is the top shelf?

Answer 1

PART A - So the ruler is 22.86 centimeters tall, and after measuring with an inch ruler, is also 9 inches tall.
ruler = 22.86cm
ruler = 9 in
You can equate 22.86cm and 9in because they both equal the length of the ruler (transitive property).
22.86cm = 9in
Then you can write a proportionality equation.
$\frac{22.86cm}{9in} = \frac{x}{1in}$

Part B - 
Cross multiplying,
$(9in)x = (22.86cm)1 \\ x = \frac{22.86cm}{9in}= 2.54cm/in$

Part C - We can use something called dimensional analysis - multiplying 12 cm by (1in/2.54cm) - in order to change the units from inches to cm. This is possible because 1in = 2.54cm, the fraction 1in/2.54cm = 1. And also the units cm will cancel out.
$\frac{12cm}{1} * \frac{1in}{2.54cm} = 4.72in$