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Question

Difficulty: EasyFraction Operations

A carpenter has a wooden board that is 5345 \frac{3}{4} inches wide. If he shaves off exactly 18\frac{1}{8} of an inch from the width, what is the new width of the board?

  1. 5585 \frac{5}{8} inchesAnswer
  2. B
    5125 \frac{1}{2} inches
  3. C
    5785 \frac{7}{8} inches
  4. D
    5145 \frac{1}{4} inches

Answer

The new width of the board is 5585 \frac{5}{8} inches.
To find the new width, subtract the shaved amount from the original width: 534−185 \frac{3}{4} - \frac{1}{8}. First, find a common denominator, which is 8. Convert 34\frac{3}{4} to 68\frac{6}{8}. Subtracting 18\frac{1}{8} from 5685 \frac{6}{8} gives the correct answer of 5585 \frac{5}{8} inches.

Step-by-Step Solution

1
Set up the subtraction problem based on the context.
534−185 \frac{3}{4} - \frac{1}{8}
The phrase 'shaves off' indicates subtraction from the original width.
2
Find a common denominator for the fractions 34\frac{3}{4} and 18\frac{1}{8}.
The common denominator is 88.
Fractions must have the same denominator before they can be subtracted.
3
Convert 34\frac{3}{4} to an equivalent fraction with a denominator of 88.
3×24×2=68\frac{3 \times 2}{4 \times 2} = \frac{6}{8}
Multiplying both the numerator and denominator by 22 keeps the fraction's value the same while converting the denominator.
4
Subtract the fractions.
568−18=5585 \frac{6}{8} - \frac{1}{8} = 5 \frac{5}{8}
Subtract the numerators while keeping the common denominator the same.

Key Concept

Subtracting mixed numbers with unlike denominators
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Topics

Fraction Operations

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