Question
Calculate the difference between your estimate in part A and the actual value calculated in Part B be sure to show this solution as an equation based on this difference do you think your estimate for part A was reasonable explain Part A 10 / 12 can be simplified to 5/6 we know that thought over 6 is close to 1 or 6/6 so we can round 10/12 to 1 3/8 is less than 4/8 equal 1/2 so we can round 3/8 to 1/2 estimate value of 10/12 is 1 estimate that value of 3/8 is 1/2 1 - 1/2 = 2/2 - 1/2 = 1/2 estimate value for 10/12 - 3/8 equal 1/2 Part B find a common denominator the denominators are 12 and 8 The least common multiple LCM of 12 and 8 is 24 convert each fraction to have the common denominator of 24 for 10/12 equal 10/12* 2/2 equals 20/24 for 3/8 * 3/3 equal 9/24 20 / 24 - 9 = 11 / 24 10/12 3/8 is 11/24
Answers
GPT-4o mini
To show the calculation clearly, let's first summarize the parts you provided and then calculate the difference between the estimated value in Part A and the actual value found in Part B.
### Part A:
1. **Estimate for \( \frac{10}{12} \)**:
- Simplified to \( \frac{5}{6} \) which is close to 1.
2. **Estimate for \( \frac{3}{8} \)**:
- Rounded to \( \frac{1}{2} \).
3. **Estimated difference**:
\[
1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}
\]
**Final estimate for \( \frac{10}{12} - \frac{3}{8} \)**:
\[
\frac{1}{2}
\]
### Part B:
1. **Actual calculation**:
\[
\frac{10}{12} - \frac{3}{8}
\]
- Common denominator is 24:
- Convert \( \frac{10}{12} \):
\[
\frac{10}{12} \cdot \frac{2}{2} = \frac{20}{24}
\]
- Convert \( \frac{3}{8} \):
\[
\frac{3}{8} \cdot \frac{3}{3} = \frac{9}{24}
\]
- Perform the subtraction:
\[
\frac{20}{24} - \frac{9}{24} = \frac{11}{24}
\]
### Difference Calculation:
Now, we calculate the difference between the estimated value and the actual value:
**Estimate from Part A**: \( \frac{1}{2} \)
**Actual value from Part B**: \( \frac{11}{24} \)
**Write the equation for the difference**:
\[
\text{Difference} = \text{Estimated Value} - \text{Actual Value}
\]
\[
\text{Difference} = \frac{1}{2} - \frac{11}{24}
\]
To calculate this difference, we need to convert \( \frac{1}{2} \) to have a denominator of 24:
\[
\frac{1}{2} = \frac{12}{24}
\]
Now we can substitute and calculate the difference:
\[
\text{Difference} = \frac{12}{24} - \frac{11}{24} = \frac{1}{24}
\]
### Final Result:
Thus, the final difference is:
\[
\text{Difference} = \frac{1}{24}
\]
### Reasonableness of the Estimate:
The estimate of \( \frac{1}{2} \) is relatively close to the actual value of \( \frac{11}{24} \), which is approximately \( 0.4583 \). Since \( \frac{1}{2} = 0.5 \), the estimate is reasonable, albeit a bit higher than the actual difference. Depending on context, this level of accuracy may be acceptable, or it may invite further refinement in estimation techniques.
### Part A:
1. **Estimate for \( \frac{10}{12} \)**:
- Simplified to \( \frac{5}{6} \) which is close to 1.
2. **Estimate for \( \frac{3}{8} \)**:
- Rounded to \( \frac{1}{2} \).
3. **Estimated difference**:
\[
1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}
\]
**Final estimate for \( \frac{10}{12} - \frac{3}{8} \)**:
\[
\frac{1}{2}
\]
### Part B:
1. **Actual calculation**:
\[
\frac{10}{12} - \frac{3}{8}
\]
- Common denominator is 24:
- Convert \( \frac{10}{12} \):
\[
\frac{10}{12} \cdot \frac{2}{2} = \frac{20}{24}
\]
- Convert \( \frac{3}{8} \):
\[
\frac{3}{8} \cdot \frac{3}{3} = \frac{9}{24}
\]
- Perform the subtraction:
\[
\frac{20}{24} - \frac{9}{24} = \frac{11}{24}
\]
### Difference Calculation:
Now, we calculate the difference between the estimated value and the actual value:
**Estimate from Part A**: \( \frac{1}{2} \)
**Actual value from Part B**: \( \frac{11}{24} \)
**Write the equation for the difference**:
\[
\text{Difference} = \text{Estimated Value} - \text{Actual Value}
\]
\[
\text{Difference} = \frac{1}{2} - \frac{11}{24}
\]
To calculate this difference, we need to convert \( \frac{1}{2} \) to have a denominator of 24:
\[
\frac{1}{2} = \frac{12}{24}
\]
Now we can substitute and calculate the difference:
\[
\text{Difference} = \frac{12}{24} - \frac{11}{24} = \frac{1}{24}
\]
### Final Result:
Thus, the final difference is:
\[
\text{Difference} = \frac{1}{24}
\]
### Reasonableness of the Estimate:
The estimate of \( \frac{1}{2} \) is relatively close to the actual value of \( \frac{11}{24} \), which is approximately \( 0.4583 \). Since \( \frac{1}{2} = 0.5 \), the estimate is reasonable, albeit a bit higher than the actual difference. Depending on context, this level of accuracy may be acceptable, or it may invite further refinement in estimation techniques.