Question

Elliot is moving a table through a doorway. The table is 2 and StartFraction 5 Over 8 EndFraction ft wide and the doorway is 2 and three-fourths ft wide. Which statement explains if the table will fit through the door?

The table will fit because 2 and StartFraction 5 Over 8 EndFraction < 2 and three-fourths.
The table will fit because 2 and StartFraction 5 Over 8 EndFraction > 2 and three-fourths.
The table will not fit because 2 and StartFraction 5 Over 8 EndFraction < 2 and three-fourths.
The table will not fit because 2 and StartFraction 5 Over 8 EndFraction > 2 and three-fourths.

Answer 1

To determine if the table will fit through the doorway, we need to compare the widths of both.

1. The width of the table is \(2 \frac{5}{8}\) ft, which can be converted to an improper fraction:
\[
2 \frac{5}{8} = \frac{16}{8} + \frac{5}{8} = \frac{21}{8} \text{ ft}
\]

2. The width of the doorway is \(2 \frac{3}{4}\) ft, which can also be converted to an improper fraction:
\[
2 \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \text{ ft}
\]

Next, we need to find a common denominator to compare \(\frac{21}{8}\) and \(\frac{11}{4}\). The least common denominator of 8 and 4 is 8.

3. Convert \(\frac{11}{4}\) to have a denominator of 8:
\[
\frac{11}{4} = \frac{11 \times 2}{4 \times 2} = \frac{22}{8}
\]

Now we can compare both fractions:
- Table width: \(\frac{21}{8} \text{ ft}\)
- Doorway width: \(\frac{22}{8} \text{ ft}\)

Since \( \frac{21}{8} < \frac{22}{8} \), this means that:

\[
2 \frac{5}{8} < 2 \frac{3}{4}
\]

Thus, the correct statement is:
**The table will fit because \(2 \frac{5}{8} < 2 \frac{3}{4}\).**