Examkin

Question

Difficulty: MediumFraction Operations

A tailor has a bolt of fabric that is 201420\frac{1}{4} yards long. He cuts 5345\frac{3}{4} yards of fabric to make a suit jacket and another 3583\frac{5}{8} yards to make a pair of trousers. How many yards of fabric are remaining on the bolt?

  1. 107810\frac{7}{8}Answer
  2. B
    1171211\frac{7}{12}
  3. C
    181818\frac{1}{8}
  4. D
    111811\frac{1}{8}

Answer

107810\frac{7}{8}
The correct answer is found by first calculating the total fabric used (534+358=9385\frac{3}{4} + 3\frac{5}{8} = 9\frac{3}{8} yards). Subtracting this from the original 201420\frac{1}{4} yards requires converting to a common denominator (2028−93820\frac{2}{8} - 9\frac{3}{8}) and then borrowing from the whole number (19108−93819\frac{10}{8} - 9\frac{3}{8}) to get exactly 107810\frac{7}{8} yards.

Step-by-Step Solution

1
Find the total amount of fabric used by adding 5345\frac{3}{4} and 3583\frac{5}{8}.
534+358=568+358=8118=9385\frac{3}{4} + 3\frac{5}{8} = 5\frac{6}{8} + 3\frac{5}{8} = 8\frac{11}{8} = 9\frac{3}{8} yards.
Before finding the remaining amount, the total amount removed from the bolt must be calculated by finding a common denominator.
2
Subtract the total used fabric from the original length of the bolt.
2014−938=2028−93820\frac{1}{4} - 9\frac{3}{8} = 20\frac{2}{8} - 9\frac{3}{8}.
Subtracting the used amount from the initial amount determines how much fabric is left.
3
Borrow from the whole number to complete the subtraction.
19108−938=107819\frac{10}{8} - 9\frac{3}{8} = 10\frac{7}{8} yards.
Since 22 is less than 33 in the numerators, 11 whole (8/88/8) must be borrowed from 2020 to make the subtraction possible.

Key Concept

Adding and subtracting mixed numbers with unlike denominators, including borrowing.
Rate this question

Topics

Fraction Operations

More questions from this topic