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 = 12 27 and 3 5 = 12 20 .
Subtract the fractions: 12 27 − 12 20 = 12 7 .
The remaining length of the cording is 12 7 f t .
Explanation
Understanding the problem We need to find out how much cording is left after cutting a piece from a longer piece. The initial length of the cording is 2 4 1 feet, and the length of the piece that was cut off is 1 3 2 feet. To find the remaining length, we need to subtract the length of the cut piece from the initial length.
Converting to improper fractions First, convert the mixed numbers to improper fractions. 2 4 1 = 4 2 × 4 + 1 = 4 8 + 1 = 4 9 1 3 2 = 3 1 × 3 + 2 = 3 3 + 2 = 3 5
Subtracting the lengths Now, subtract the length of the cording cut from the initial 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: 4 9 = 4 × 3 9 × 3 = 12 27 3 5 = 3 × 4 5 × 4 = 12 20 Now we can subtract: 12 27 − 12 20 = 12 27 − 20 = 12 7
Finding the remaining length The remaining length of the cording is 12 7 feet.
Examples
Imagine you are making a friendship bracelet. You start with a piece of embroidery thread that is 2 4 1 feet long. You need to cut off 1 3 2 feet to make the bracelet. The calculation we just did tells you how much thread you will have left over after making the bracelet. This kind of subtraction is useful in many crafting and building projects where you need to calculate leftover materials.
