avid and Patt each decomposed $$ 1 \frac{3}{8} $$. David wrote $$ 1+\frac{1}{8}+\frac{3}{8} $$. Patti wrote $$ \frac{4}{8}+\frac{2}{8}+\frac{5}{8} $$. Who is correct? Explain your reasoni Only David is correct. $$ 1+\frac{1}{8}+\frac{3}{8}=1 \frac{3}{8} $$, but $$ \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=\frac{11}{8} $$ Ony Patti is correct $$ \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=1 \frac{3}{8} $$, but $$ 1+\frac{1}{8}+\frac{3}{8}=\frac{12}{8} $$. Both Devid and Patti are correct. $$ 1+\frac{1}{8}+\frac{3}{8}=1 \frac{3}{8} $$, and $$ \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=1 \frac{3}{8} $$. Neither David nor Pathi is correct. $$ 1+\frac{1}{8}+\frac{3}{8}=\frac{12}{8} $$, and $$ \frac{4}{8}+\frac{2}{8}+\frac{5}{8}=\frac{11}{8} $$.

Question

UpStudy AI · Accepted Answer

Let's analyze the decompositions provided by David and Patti to determine who is correct.

### Original Fraction:
$$ 1 \frac{3}{8} = \frac{11}{8} $$

### David's Decomposition:
$$ 1 + \frac{1}{8} + \frac{3}{8} $$

**Calculation:**
$$
1 + \frac{1}{8} + \frac{3}{8} = \frac{8}{8} + \frac{1}{8} + \frac{3}{8} = \frac{12}{8} = 1 \frac{1}{2}
$$

**Conclusion:**
David's decomposition sums up to $$1 \frac{1}{2}$$, which is $$\frac{12}{8}$$. This does **not** equal the original fraction $$1 \frac{3}{8}$$.

### Patti's Decomposition:
$$ \frac{4}{8} + \frac{2}{8} + \frac{5}{8} $$

**Calculation:**
$$
\frac{4}{8} + \frac{2}{8} + \frac{5}{8} = \frac{11}{8} = 1 \frac{3}{8}
$$

**Conclusion:**
Patti's decomposition accurately sums up to $$1 \frac{3}{8}$$, which matches the original fraction.

### Summary of Options:

1. **Only David is correct.**
   - **Incorrect.** David's sum is $$1 \frac{1}{2}$$, not $$1 \frac{3}{8}$$.

2. **Only Patti is correct.**
   - **Correct.** Patti's sum correctly equals $$1 \frac{3}{8}$$.

3. **Both David and Patti are correct.**
   - **Incorrect.** Only Patti's decomposition is accurate.

4. **Neither David nor Patti is correct.**
   - **Incorrect.** Patti's decomposition is correct.

**Final Answer:**

**Only Patti is correct.** 
$$
\frac{4}{8} + \frac{2}{8} + \frac{5}{8} = \frac{11}{8} = 1 \frac{3}{8}
$$
However, 
$$
1 + \frac{1}{8} + \frac{3}{8} = \frac{12}{8} = 1 \frac{1}{2} \neq 1 \frac{3}{8}
$$
Only Patti is correct.

avid and Patt each decomposed . David wrote . Patti wrote . Who is correct? Explain your reasoni

Only David is correct. , but

Ony Patti is correct , but .

Both Devid and Patti are correct. , and .

Neither David nor Pathi is correct. , and .

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Solución

Original Fraction:

David’s Decomposition:

Patti’s Decomposition:

Summary of Options:

Beyond the Answer

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avid and Patt each decomposed . David wrote . Patti wrote . Who is correct? Explain your reasoni Only David is correct. , but Ony Patti is correct , but . Both Devid and Patti are correct. , and . Neither David nor Pathi is correct. , and .