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

Answer 1

### Part A: Estimating \( \frac{10}{12} - \frac{3}{8} \)

**Step 1: Find Benchmark Values**

- For \( \frac{10}{12} \): This fraction simplifies to \( \frac{5}{6} \). A benchmark value for \( \frac{5}{6} \) is about \( 1 \) since \( \frac{5}{6} \) is close to \( 1 \).

- For \( \frac{3}{8} \): A benchmark value for \( \frac{3}{8} \) is about \( \frac{1}{4} \), which is \( 0.25 \).

**Step 2: Estimate Each Fraction**

- Estimated value of \( \frac{10}{12} \approx 1 \)
- Estimated value of \( \frac{3}{8} \approx 0.25 \)

**Step 3: Calculate the Final Estimate**

Now we can perform the estimation:

\[
1 - 0.25 = 0.75
\]

**Final Estimate:**
\[
\frac{10}{12} - \frac{3}{8} \approx 0.75
\]

---

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

**Step 1: Find a Common Denominator**

The denominators are \( 12 \) and \( 8 \). The least common multiple of \( 12 \) and \( 8 \) is \( 24 \).

**Step 2: Convert Each Fraction**

Convert \( \frac{10}{12} \) to a fraction with a denominator of \( 24 \):

\[
\frac{10}{12} = \frac{10 \times 2}{12 \times 2} = \frac{20}{24}
\]

Convert \( \frac{3}{8} \) to a fraction with a denominator of \( 24 \):

\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\]

**Step 3: Subtract the Fractions**

Now perform the subtraction:

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

**Final Solution:**
\[
\frac{10}{12} - \frac{3}{8} = \frac{11}{24}
\]