By what number should `2 3/5` be multiplied to get `1 6/7`

Options

A. `1 5/7`
B. `5/7`
C. `1 1/7`
D. `1/7`

Answer

To solve the problem of finding the number by which \(2 \frac{3}{5}\) should be multiplied to get \(1 \frac{6}{7}\), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both mixed numbers into improper fractions.

For \(2 \frac{3}{5}\):
\[ 2 \frac{3}{5} = \frac{(2 \times 5) + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} \]

For \(1 \frac{6}{7}\):
\[ 1 \frac{6}{7} = \frac{(1 \times 7) + 6}{7} = \frac{7 + 6}{7} = \frac{13}{7} \]

### Step 2: Set Up the Equation
Now, we need to set up the equation to find the unknown number \(x\):
\[ \frac{13}{5} \times x = \frac{13}{7} \]

### Step 3: Solve for \(x\)
To isolate \(x\), we can multiply both sides by the reciprocal of \(\frac{13}{5}\):
\[ x = \frac{13}{7} \div \frac{13}{5} \]
This can be rewritten as:
\[ x = \frac{13}{7} \times \frac{5}{13} \]

### Step 4: Simplify the Expression
Now, we can simplify:
\[ x = \frac{13 \times 5}{7 \times 13} = \frac{5}{7} \]

### Conclusion
Thus, the number by which \(2 \frac{3}{5}\) should be multiplied to get \(1 \frac{6}{7}\) is:
\[ \frac{5}{7} \]

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