By what number should `1 3/4` be divided to get `2 1/2`?

Options

A. `3/7`
B. `1 2/5`
C. `7/10`
D. ` 1 3/7`

Answer

To solve the problem of finding the number by which \(1 \frac{3}{4}\) should be divided to get \(2 \frac{1}{2}\), we can follow these steps:

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- Convert \(1 \frac{3}{4}\) to an improper fraction:
\[ 1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \]
- Convert \(2 \frac{1}{2}\) to an improper fraction:
\[ 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]

2. **Set Up the Equation**:
- We need to find a number \(x\) such that:
\[ \frac{7}{4} \div x = \frac{5}{2} \]
- This can be rewritten as:
\[ \frac{7}{4} = x \cdot \frac{5}{2} \]

3. **Cross Multiply**:
- Rearranging gives us:
\[ 7 \cdot 2 = 4 \cdot 5 \cdot x \]
- Simplifying this:
\[ 14 = 20x \]

4. **Solve for \(x\)**:
- Divide both sides by 20:
\[ x = \frac{14}{20} \]
- Simplifying the fraction:
\[ x = \frac{7}{10} \]

5. **Conclusion**:
- Therefore, \(1 \frac{3}{4}\) should be divided by \(\frac{7}{10}\) to get \(2 \frac{1}{2}\).

### Final Answer:
The number by which \(1 \frac{3}{4}\) should be divided to get \(2 \frac{1}{2}\) is \(\frac{7}{10}\).