Question

dallas discovered some scrap wood while cleaning out his garage. he found 3 boards that were $3\frac{1}{4}$ feet long, 2 boards that were $4\frac{1}{2}$ feet long, and 1 board that was 5 feet long. if he lines up all of the boards end - to - end, what is the total length?\
\\(\bigcirc\\ 19\frac{5}{8}\\) feet\
\\(\bigcirc\\ 20\frac{1}{8}\\) feet\
\\(\bigcirc\\ 13\frac{1}{8}\\) feet\
\\(\bigcirc\\ 25\frac{5}{8}\\) feet

Explanation:

Step1: Calculate length of 3 boards

First convert $3\frac{3}{4}$ to improper fraction: $3\frac{3}{4}=\frac{15}{4}$. Multiply by 3:
$\frac{15}{4} \times 3 = \frac{45}{4}$

Step2: Calculate length of 2 boards

Convert $4\frac{2}{3}$ to improper fraction: $4\frac{2}{3}=\frac{14}{3}$. Multiply by 2:
$\frac{14}{3} \times 2 = \frac{28}{3}$

Step3: Add the 5-foot board

The single board is 5, so rewrite as $\frac{5}{1}$. Now find a common denominator (12) for all fractions:
$\frac{45}{4} = \frac{135}{12}$, $\frac{28}{3} = \frac{112}{12}$, $\frac{5}{1} = \frac{60}{12}$

Step4: Sum all lengths

Add the converted fractions:
$\frac{135}{12} + \frac{112}{12} + \frac{60}{12} = \frac{135+112+60}{12} = \frac{307}{12}$

Step5: Convert to mixed number

Divide 307 by 12: $307 = 12 \times 25 + 7$, so $\frac{307}{12}=25\frac{7}{12}$

Answer:

25 $\frac{7}{12}$ feet