Question

what is the total length of the roll of sheet metal, shown below, in inches?

dimensions shown:

• leftmost segment: \\(6\frac{1.5}{8}\\) inches
• second segment: \\(9\frac{5}{8}\\) inches
• middle segment: \\(21\frac{7}{8}\\) inches
• fourth segment: \\(9\frac{5}{8}\\) inches
• rightmost segment: \\(6\frac{1.5}{8}\\) inches

options:

• 53.00 inches
• 53.25 inches
• 53.50 inches
• 53.75 inches

Explanation:

Identify the given segment lengths

We need to find the total length of the roll of sheet metal by adding the lengths of the five individual segments shown in the diagram:

• Segment 1: \(6\frac{1.5}{8}\text{ inches}\)
• Segment 2: \(9\frac{5}{8}\text{ inches}\)
• Segment 3: \(21\frac{7}{8}\text{ inches}\)
• Segment 4: \(9\frac{5}{8}\text{ inches}\)
• Segment 5: \(6\frac{1.5}{8}\text{ inches}\)

Convert mixed numbers with decimals to standard fractions

Using the Fraction to Decimal Conversion knowledge point, we can rewrite the fractional parts to make addition easier.
For the first and last segments, the fraction is \(\frac{1.5}{8}\). We can multiply the numerator and denominator by \(2\) to get a standard fraction:

$$\frac{1.5 \times 2}{8 \times 2} = \frac{3}{16}$$

Thus, the lengths are:

• Segment 1: \(6\frac{3}{16}\text{ inches}\)
• Segment 2: \(9\frac{5}{8} = 9\frac{10}{16}\text{ inches}\)
• Segment 3: \(21\frac{7}{8} = 21\frac{14}{16}\text{ inches}\)
• Segment 4: \(9\frac{5}{8} = 9\frac{10}{16}\text{ inches}\)
• Segment 5: \(6\frac{3}{16}\text{ inches}\)

Add the mixed numbers

Using the Mixed Number Addition knowledge point, we sum the whole numbers and the fractional parts separately.

Sum of the whole numbers:

$$6 + 9 + 21 + 9 + 6 = 51$$

Sum of the fractional parts:

$$\frac{3}{16} + \frac{10}{16} + \frac{14}{16} + \frac{10}{16} + \frac{3}{16} = \frac{3 + 10 + 14 + 10 + 3}{16} = \frac{40}{16}$$

Simplify the fractional sum

Convert the improper fraction \(\frac{40}{16}\) to a mixed number:

$$\frac{40}{16} = 2\frac{8}{16} = 2\frac{1}{2} = 2.5$$

Calculate the final total length

Combine the whole number sum and the simplified fractional sum:

$$51 + 2.5 = 53.5\text{ inches}$$

This corresponds to \(53.50\text{ inches}\).

Answer:

• 53.00 inches
• 53.25 inches
• 53.50 inches (Correct answer)
• 53.75 inches