An iron rod is $12 \frac{1}{2} m$ long. If $7 \frac{3}{4} m$ length is cut off from one end of the rod, what is the length of the rod remaining?
Answer (1)
Convert the mixed fractions to improper fractions: 12 2 1 = 2 25 and 7 4 3 = 4 31 .
Find a common denominator to subtract the fractions: 2 25 = 4 50 .
Subtract the lengths: 4 50 − 4 31 = 4 19 .
Convert the result back to a mixed fraction: 4 19 = 4 4 3 . The length of the rod remaining is 4 4 3 m .
Explanation
Understanding the Problem We are given that an iron rod is 12 2 1 meters long and a piece of 7 4 3 meters is cut off from one end. We need to find the length of the remaining rod. This is a subtraction problem where we subtract the length of the piece cut off from the original length of the rod.
Converting to Improper Fractions First, let's convert the mixed fractions to improper fractions. We have:
12 2 1 = 2 12 × 2 + 1 = 2 24 + 1 = 2 25 meters
7 4 3 = 4 7 \t × 4 + 3 = 4 28 + 3 = 4 31 meters
Subtracting the Lengths Now, subtract the length cut off from the original length:
2 25 − 4 31
Finding a Common Denominator To subtract these fractions, we need a common denominator. The least common denominator of 2 and 4 is 4. So, we convert 2 25 to a fraction with denominator 4:
2 25 = 2 \t × 2 25 \t × 2 = 4 50
Performing the Subtraction Now we can subtract:
4 50 − 4 31 = 4 50 − 31 = 4 19 meters
Converting Back to a Mixed Fraction Finally, convert the improper fraction 4 19 back to a mixed fraction:
4 19 = 4 4 3 meters
So, the length of the remaining rod is 4 4 3 meters.
Final Answer The length of the rod remaining is 4.75 meters.
Examples
Imagine you are building a bookshelf and you have a wooden plank that is 12 2 1 feet long. You need to cut off a piece that is 7 4 3 feet long to fit another part of the shelf. Calculating the remaining length helps you determine if the remaining piece is long enough for another shelf component. This type of subtraction is crucial in carpentry, construction, and any situation where you need to measure and cut materials to specific sizes. Understanding fractions and subtraction allows for precise adjustments and efficient use of materials.
