Lucy saws a wooden rod into two pieces. The larger piece is 7 3/4 inches long. The original rod was 9 1/8 inches long. How many inches long is the resulting smaller piece?
A. 2
B. 2 5/8
C. 1 3/8
D. 16 7/8
I assume it's 1 3/8. Im just too lazy to solve it;)
To find the length of the resulting smaller piece, we can subtract the length of the larger piece from the length of the original rod.
Original rod length: 9 1/8 inches
Larger piece length: 7 3/4 inches
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 8.
9 1/8 - 7 3/4
To subtract the whole numbers, we can subtract 7 from 9:
9 - 7 = 2
Now, let's subtract the fractions:
1/8 - 3/4
Since the denominators are the same, we can subtract the numerators:
1 - 3 = -2
The result is -2/8.
Now let's simplify the fraction:
-2/8 = -1/4
The resulting smaller piece has a length of -1/4 inches.
Since the length of a piece cannot be negative, we made an error in our calculations. Let's correct it:
To find the length of the smaller piece, we can subtract the length of the larger piece from the length of the original rod:
9 1/8 - 7 3/4
Again, we need to find a common denominator. The common denominator is 8.
9 1/8 - 7 3/4
To subtract the whole numbers, we can subtract 7 from 9:
9 - 7 = 2
Now, let's subtract the fractions:
1/8 - 3/4
Since the denominators are the same, we can subtract the numerators:
1 - 3 = -2
The result is -2/8.
Now let's simplify the fraction:
-2/8 = -1/4
This is the same answer we obtained earlier. It seems like we made a mistake in our calculations.
Apologies for the confusion. To get the correct answer, we should follow these steps:
1. Convert the mixed numbers to improper fractions:
9 1/8 = (9 * 8 + 1) / 8 = 73/8
7 3/4 = (7 * 4 + 3) / 4 = 31/4
2. Subtract the numerators:
73/8 - 31/4
To subtract fractions, we need a common denominator. In this case, it is 8:
73/8 - 62/8 = 11/8
The resulting smaller piece has a length of 11/8 inches.
To convert this improper fraction to a mixed number, divide the numerator (11) by the denominator (8):
11 ÷ 8 = 1 with a remainder of 3
So, the answer is 1 3/8 inches.
Therefore, the correct answer to the question is option C. 1 3/8 inches.