Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 and StartFraction 5 over 8 EndFraction inches thick. What was her error?

Question

7 (2 and StartFraction 5 over 8 EndFraction). 7 (2 + StartFraction 5 over 8 EndFraction). 14 + StartFraction 5 over 8 EndFraction. 14 and StartFraction 5 over 8 EndFraction

The fraction was not simplified in the last step.
Seven was not multiplied by StartFraction 5 over 8 EndFraction.
There should be a subtraction step, not an addition step.
Two should have been multiplied by StartFraction 5 over 8 EndFraction.

Answer 1

To determine Giovanna's error in her calculations for the height of the stack of 7 books, let's break down the steps correctly.

1. Each book is 2 and \( \frac{5}{8} \) inches thick. This can be converted to an improper fraction: \[ 2 \text{ and } \frac{5}{8} = \frac{16}{8} + \frac{5}{8} = \frac{21}{8} \]

2. To find the total height of 7 books: \[ 7 \times \frac{21}{8} \]

   This can be calculated as: \[ 7 \times \frac{21}{8} = \frac{147}{8} \]

3. Now converting \( \frac{147}{8} \) back to a mixed number:

   • Dividing 147 by 8 gives 18 with a remainder: \[ 147 \div 8 = 18 \quad \text{(remainder 3)} \]
   • This means: \[ \frac{147}{8} = 18 \text{ and } \frac{3}{8} \]

Giovanna's mistake in her calculation was that Seven was not multiplied by \( \frac{5}{8} \) when she went through her steps, meaning she only added the whole numbers and didn't account for the fraction part correctly.

Thus, the answer is: Seven was not multiplied by \( \frac{5}{8} \).