Question
Marcus has a board that is \( 7 \frac{1}{4} \) feet long. If he cuts off a piece that is \( 2 \frac{1}{2} \) feet long, how long will the board be?
Ask by Chambers Page. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The board will be \(4\frac{3}{4}\) feet long.
Solution
Calculate or simplify the expression \( 7\frac{1}{4}-2\frac{1}{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(7\frac{1}{4}-2\frac{1}{2}\)
- step1: Convert the expressions:
\(\frac{29}{4}-\frac{5}{2}\)
- step2: Reduce fractions to a common denominator:
\(\frac{29}{4}-\frac{5\times 2}{2\times 2}\)
- step3: Multiply the numbers:
\(\frac{29}{4}-\frac{5\times 2}{4}\)
- step4: Transform the expression:
\(\frac{29-5\times 2}{4}\)
- step5: Multiply the numbers:
\(\frac{29-10}{4}\)
- step6: Subtract the numbers:
\(\frac{19}{4}\)
The board will be \(4\frac{3}{4}\) feet long after Marcus cuts off the piece that is \(2\frac{1}{2}\) feet long.
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Simplify this solution Beyond the Answer
To find out how long the board will be after cutting off a piece, you'll want to subtract \( 2 \frac{1}{2} \) from \( 7 \frac{1}{4} \). First, convert both mixed numbers to improper fractions: - \( 7 \frac{1}{4} = \frac{29}{4} \) - \( 2 \frac{1}{2} = \frac{5}{2} = \frac{10}{4} \) (when the denominators are the same) Now, subtract the fractions: \[ \frac{29}{4} - \frac{10}{4} = \frac{19}{4} \] Convert \( \frac{19}{4} \) back to a mixed number. \( 19 \div 4 = 4\) remainder \( 3\), so it becomes \( 4 \frac{3}{4} \). Thus, after cutting off \( 2 \frac{1}{2} \) feet, the board will be \( 4 \frac{3}{4} \) feet long.
