Tom bought a board that was 7/8 of a yard long. He cut off 1/2 of a yard. How much was left?
The correct answer and explanation is :
Tom bought a board that was 7/8 of a yard long. After buying the board, he cut off 1/2 of a yard. To determine how much of the board was left after the cut, we need to subtract the length that was cut off from the total length of the board.
Step 1: Convert the fractions to a common denominator
We are given two fractions: 7/8 and 1/2. In order to subtract these fractions, we need to express them with a common denominator. The denominators of 8 and 2 are different, so we need to find the least common denominator (LCD).
The least common denominator between 8 and 2 is 8. To make 1/2 have a denominator of 8, we multiply both the numerator and the denominator by 4:
[
1/2 = (1 \times 4) / (2 \times 4) = 4/8
]
Now, we have two fractions with a denominator of 8: 7/8 and 4/8.
Step 2: Subtract the fractions
Now that both fractions have the same denominator, we can subtract them directly. We subtract the numerators while keeping the denominator the same:
[
7/8 – 4/8 = (7 – 4) / 8 = 3/8
]
Step 3: Conclusion
So, after Tom cut off 1/2 of a yard, the length of the board that was left is 3/8 of a yard.
Explanation
This problem is a simple example of fraction subtraction. The key step in solving it was to first find a common denominator between 7/8 and 1/2, which allowed us to subtract the two fractions directly. Understanding how to convert fractions and finding the least common denominator is crucial when working with fractions. By performing this calculation, we can determine the exact amount of the board that remained after the cut.