Tim is $56 \frac{3}{4}$ inches tall. Joey is $1 \frac{1}{2}$ inches taller than Tim, and Jane is $1 \frac{1}{5}$ inches taller than Joey. How tall is Jane?
Tim's height is given as \(56 \frac{3}{4}\) inches. Joey is \(1 \frac{1}{2}\) inches taller than Tim, and Jane is \(1 \frac{1}{5}\) inches taller than Joey. We need to find Jane's total height in inches. To make calculations easier, we first convert the mixed numbers into decimals:
Joey's height is determined by adding the difference of \(1.5\) inches to Tim's height:
\[\text{Joey's height} = 56.75 + 1.5 = 58.25 \text{ inches.}\]
Jane's height is determined by adding the difference of \(1.2\) inches to Joey's height:
\[\text{Jane's height} = 58.25 + 1.2 = 59.45 \text{ inches.}\]
To express this as a mixed number, we note that \(0.45 = \frac{45}{100} = \frac{9}{20}\). Thus, Jane's height is \(59 \frac{9}{20}\) inches.
In real life, measuring heights accurately is a common task for doctors, tailors, or coaches. By breaking down measurements into a series of additions, you can easily track incremental changes. For instance, if you are keeping track of growth charts for children, you can use simple arithmetic to update records each time a measurement is taken, ensuring that all data is precise and easy to compare. This systematic approach is essential in any field involving standardized measurements.