Zoe had a board 5 1/4 feet long. She cut off a piece. Now the board is 3 5/6 feet long. How long was the piece she cut off?
1 2/6
12/16
To find the length of the piece Zoe cut off, we subtract the final length of the board from the original length. Here's how we can solve it step by step:
1. Convert the mixed numbers (5 1/4 and 3 5/6) into improper fractions:
- 5 1/4 = (4 * 5 + 1) / 4 = 21 / 4
- 3 5/6 = (6 * 3 + 5) / 6 = 23 / 6
2. Subtract the final length from the original length:
21/4 - 23/6
To find a common denominator for 4 and 6, we need to find their least common multiple (LCM), which is 12 in this case.
3. Rewrite the fractions 21/4 and 23/6 with the common denominator of 12:
- 21/4 = (21 * 3) / (4 * 3) = 63/12
- 23/6 = (23 * 2) / (6 * 2) = 46/12
4. Subtract the fractions:
63/12 - 46/12 = (63 - 46) / 12 = 17/12
The result, 17/12, represents the length of the piece Zoe cut off. However, let's convert it back to mixed number form for convenience.
5. Convert 17/12 to a mixed number:
Divide the numerator by the denominator: 17 ÷ 12 = 1 remainder 5
The mixed number is 1 5/12.
Therefore, Zoe cut off a piece of the board that was 1 5/12 feet long.
5 3/12 - 3 10/12
is
4 15/12 - 3 10/12
is
1 5/12