Please anyone to help me solve this question
A piece of copper wire is 52 2/3 m long. If each piece has been cut of 3/4 from it. What length will remain after cutting pieces? math question
Divide it out, then check the remainder.
We would be happy to check your answer :)
To solve this question, we need to find out how many pieces can be cut from the original length of the copper wire and then calculate the remaining length.
Let's break it down step by step:
Step 1: Convert the mixed number to an improper fraction.
- 52 2/3 can be written as (3 × 52 + 2) / 3 = 158/3
Step 2: Calculate the number of pieces that can be cut.
Divide the length of the copper wire by the length of each cut piece:
- (158/3) / (3/4) = (158/3) × (4/3)
- Invert the denominator and multiply:
- (158/3) × (4/3) = (158 × 4) / (3 × 3) = 632/9
Step 3: Calculate the remaining length.
- The remaining length is the original length minus the total length of all the cut pieces:
- Remaining length = (158/3) - (632/9)
Now, let's simplify the remaining length:
Step 4: Convert the remaining length to a mixed number.
- (158/3) = 52 2/3 is the original length
- (632/9) can be written as 70 2/9
Step 5: Calculate the remaining length by subtracting the total cut pieces from the original length.
- Remaining length = 52 2/3 - 70 2/9
To subtract these mixed numbers:
Step 6: Find a common denominator.
- The common denominator is 3 and 9 = 9 (3 × 9 = 27)
Step 7: Convert both mixed numbers to fractions with the common denominator.
- 52 2/3 = (52 × 9 + 2) / 27 = 470/27
- 70 2/9 = (70 × 3 + 2) / 27 = 212/27
Step 8: Subtract the fractions.
- Remaining length = 470/27 - 212/27
- Remaining length = (470 - 212) / 27 = 258/27
Finally, let's simplify the remaining length:
Step 9: Convert the fraction to a mixed number.
- Dividing 258 by 27, we get 9 with a remainder of 3, so the fraction can be written as 9 3/27.
Therefore, the remaining length of the copper wire after cutting pieces is 9 3/27 meters, which can be further simplified to 9 1/9 meters.