An upholsterer cuts a $1 \frac{2}{3}$ foot piece of cording from a piece that is $2 \frac{1}{4}$ feet long. How much cording is left?
A. $\frac{7}{12} ft$
B. $1 \frac{5}{12} ft$
C. $1 \frac{7}{12} ft$
D. $3 \frac{11}{12} ft
Answer (1)
Convert the mixed numbers to improper fractions: 2 4 1 = 4 9 and 1 3 2 = 3 5 .
Find a common denominator to subtract the fractions: 4 9 − 3 5 = 12 27 − 12 20 .
Subtract the fractions: 12 27 − 12 20 = 12 7 .
The remaining length of cording is 12 7 f t .
Explanation
Problem Analysis Let's analyze the problem. We are given an initial length of cording and the length of a piece that is cut from it. We need to find the length of the remaining cording. This is a subtraction problem.
Converting Mixed Numbers to Improper Fractions First, we need to convert the mixed numbers to improper fractions. The initial length is 2 4 1 feet, which is equal to 4 ( 2 × 4 ) + 1 = 4 8 + 1 = 4 9 feet. The length of the piece cut is 1 3 2 feet, which is equal to 3 ( 1 × 3 ) + 2 = 3 3 + 2 = 3 5 feet.
Finding a Common Denominator Now, we subtract the length of the cut piece from the original length: 4 9 − 3 5 . To subtract these fractions, we need a common denominator. The least common multiple of 4 and 3 is 12. So, we convert both fractions to have a denominator of 12.
Subtracting the Fractions 4 9 = 4 × 3 9 × 3 = 12 27 and 3 5 = 3 × 4 5 × 4 = 12 20 . Now we can subtract: 12 27 − 12 20 = 12 27 − 20 = 12 7 feet.
Final Answer The remaining length of the cording is 12 7 feet. Comparing this to the given options, we see that option A is 12 7 ft.
Examples
Imagine you're making a friendship bracelet. You start with a piece of embroidery floss that's 2 4 1 feet long. You need to cut off 1 3 2 feet to make a specific pattern. The calculation we just did tells you how much floss you'll have left to finish your bracelet or add more designs. This kind of subtraction with fractions is useful in many crafting and sewing projects where you need to measure and cut materials accurately.
