Estimate the following difference by replacing each fraction with 0, 12, or 1.
7/8−6/11
1 - 1/2 = 1/2
To estimate the difference between 7/8 and 6/11, we can replace each fraction with 0, 12, or 1:
Replacing 7/8:
- 0: 0/8 = 0
- 12: 12/8 = 1.5
- 1: 1/8 = 0.125
Replacing 6/11:
- 0: 6/0 = undefined
- 12: 6/12 = 0.5
- 1: 6/11 ≈ 0.545 (rounded to three decimal places)
Therefore, the estimated difference between 7/8 and 6/11 is:
- When replacing both fractions with 0: 0 - 0 = 0
- When replacing 7/8 with 12 and 6/11 with 1: 1.5 - 0.545 = 0.955 (rounded to three decimal places)
- When replacing both fractions with 1: 0.125 - 0.545 ≈ -0.42 (rounded to two decimal places)
Note: These are only rough estimates and may not be exactly accurate, but they can give you an idea of the difference between the fractions.
To estimate the difference of 7/8 - 6/11 by replacing each fraction with 0, 12, or 1, you can follow these steps:
1. Convert both fractions to a common denominator. In this case, the common denominator will be 8 * 11 = 88.
2. Rewrite the fractions with the common denominator:
7/8 = (7 * 11) / (8 * 11) = 77/88
6/11 = (6 * 8) / (11 * 8) = 48/88
3. Replace each fraction with either 0, 12, or 1.
For the first fraction 77/88:
- If you replace it with 0, the fraction becomes 0/88 = 0.
- If you replace it with 12, the fraction becomes 12/88 = 3/22.
- If you replace it with 1, the fraction remains 77/88.
For the second fraction 48/88:
- If you replace it with 0, the fraction becomes 0/88 = 0.
- If you replace it with 12, the fraction becomes 12/88 = 3/22.
- If you replace it with 1, the fraction remains 48/88.
4. Perform the subtraction using the estimated fractions:
If you replaced both fractions with 0, the estimated difference would be 0 - 0 = 0.
If you replaced both fractions with 12 or 1, the estimated difference would be (3/22) - (3/22) = 0.
Therefore, regardless of the values chosen (0, 12, or 1) to replace the fractions, the estimated difference would be 0.