Question

Which values of a, b, and c correctly represent the answer in simplest form?

3 and one-fourth divided by 2 and three-eighths = a StartFraction b Over c EndFraction
a = 38, b = 14, c = 1
a = 1, b = 14, c = 38
a = 1, b = 7, c = 19
a = 19, b = 7, c = 1

Answer 1

To solve the problem, let's first convert the mixed numbers into improper fractions.

**Step 1: Convert the mixed numbers to improper fractions.**

1. **Convert \(3 \frac{1}{4}\):**
\[
3 \frac{1}{4} = 3 \times 4 + 1 = 12 + 1 = 13 \quad \text{so,}\quad 3 \frac{1}{4} = \frac{13}{4}.
\]

2. **Convert \(2 \frac{3}{8}\):**
\[
2 \frac{3}{8} = 2 \times 8 + 3 = 16 + 3 = 19 \quad \text{so,} \quad 2 \frac{3}{8} = \frac{19}{8}.
\]

**Step 2: Set up the division of fractions.**
Now we need to divide:
\[
\frac{13}{4} \div \frac{19}{8}.
\]
This is equivalent to multiplying by the reciprocal:
\[
\frac{13}{4} \times \frac{8}{19} = \frac{13 \times 8}{4 \times 19}.
\]

**Step 3: Simplify the fractions.**
Calculating:
\[
\frac{13 \times 8}{4 \times 19} = \frac{104}{76}.
\]

**Step 4: Simplify \(\frac{104}{76}\).**
To simplify, we find the greatest common divisor (GCD) of 104 and 76.

The GCD of 104 and 76 is 4. Now we can divide both the numerator and the denominator by 4:
\[
\frac{104 \div 4}{76 \div 4} = \frac{26}{19}.
\]

**Step 5: Express \(\frac{26}{19}\) in the required format.**
This fraction is already in simplest form, and we can write it as:
\[
a = 1, \quad b = 7, \quad c = 19.
\]

Now, let's compare this with the provided options:
- a = 38, b = 14, c = 1
- a = 1, b = 14, c = 38
- a = 1, b = 7, c = 19
- a = 19, b = 7, c = 1

The correct values of \( a, b, c \) that represent the answer in simplest form are:
\[
\boxed{1, 7, 19}.
\]