What should be added to `5 3/7` to get 12?

Options

A. `45/7`
B. `46/7`
C. `47/7`
D. `48/7`

Answer

To solve the problem of what should be added to \(5 \frac{3}{7}\) to get \(12\), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
First, we convert \(5 \frac{3}{7}\) into an improper fraction.
\[ 5 \frac{3}{7} = \frac{(5 \times 7) + 3}{7} = \frac{35 + 3}{7} = \frac{38}{7} \]

### Step 2: Set up the equation
Let \(x\) be the number that we need to add. We can set up the equation:
\[ \frac{38}{7} + x = 12 \]

### Step 3: Isolate \(x\)
To find \(x\), we need to isolate it on one side of the equation:
\[ x = 12 - \frac{38}{7} \]

### Step 4: Convert \(12\) to a fraction with a common denominator
Next, we convert \(12\) into a fraction with a denominator of \(7\):
\[ 12 = \frac{12 \times 7}{7} = \frac{84}{7} \]

### Step 5: Subtract the fractions
Now we can subtract the fractions:
\[ x = \frac{84}{7} - \frac{38}{7} = \frac{84 - 38}{7} = \frac{46}{7} \]

### Step 6: Conclusion
Thus, the number that should be added to \(5 \frac{3}{7}\) to get \(12\) is:
\[ \frac{46}{7} \]

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