Question

Part a estimate 10th 12 - 3/8 using benchmark values Your equation must show the estimate of each traction and the final estimate
part b
solve 10/12-3/8 show your solution as an equation


part c Calculate the difference between your estimate in part A and the actual value you calculated in Part B be sure to show your solution as an equation based on this difference do you think your estimate

Answer 1

Let's tackle each part of your question step-by-step:

### Part A: Estimate \( \frac{10}{12} - \frac{3}{8} \) using benchmark values

First, we simplify the fractions \( \frac{10}{12} \) and \( \frac{3}{8} \) to benchmark values.

1. **Estimate \( \frac{10}{12} \)**:
- \( \frac{10}{12} \) simplifies to \( \frac{5}{6} \), which is close to 1.
- We can estimate it as \( 1 \).

2. **Estimate \( \frac{3}{8} \)**:
- \( \frac{3}{8} \) is approximately \( 0.375 \).
- We can estimate it as \( 0.5 \) (or \( \frac{1}{2} \)).

Now we can perform the estimation:

\[
1 - 0.5 = 0.5
\]

**Final Estimate**: The estimate for \( \frac{10}{12} - \frac{3}{8} \) is approximately \( 0.5 \).

---

### Part B: Solve \( \frac{10}{12} - \frac{3}{8} \)

To solve this, we first need a common denominator. The least common multiple of 12 and 8 is 24.

Convert both fractions:

1. **Convert \( \frac{10}{12} \)**:
\[
\frac{10}{12} = \frac{10 \times 2}{12 \times 2} = \frac{20}{24}
\]

2. **Convert \( \frac{3}{8} \)**:
\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\]

Now perform the subtraction:

\[
\frac{20}{24} - \frac{9}{24} = \frac{20 - 9}{24} = \frac{11}{24}
\]

---

### Part C: Calculate the difference between your estimate and the actual value

We found the estimate to be \( 0.5 \) (or \( \frac{1}{2} \)) and the actual value to be \( \frac{11}{24} \).

First, we need to convert \( 0.5 \) to a fraction:
\[
0.5 = \frac{1}{2}
\]

Let's express \( \frac{1}{2} \) with a common denominator of 24:
\[
\frac{1}{2} = \frac{12}{24}
\]

Now we can find the difference:
\[
\text{Difference} = \text{Estimate} - \text{Actual Value} = \frac{12}{24} - \frac{11}{24} = \frac{1}{24}
\]

**Conclusion**: The difference between the estimate and the actual value is \( \frac{1}{24} \).

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To conclude, the estimate was slightly higher than the actual value. The estimate helped provide a quick reference point, but it was not entirely accurate in this case.