What should be added to `7 3/5` to get 18?

Options

A. `13 3/5`
B. `10 2/5`
C. `11 2/5`
D. `13 2/5`

Answer

To solve the question "What should be added to \(7 \frac{3}{5}\) to get 18?", we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \(7 \frac{3}{5}\) can be converted to an improper fraction.
To do this, multiply the whole number (7) by the denominator (5) and add the numerator (3).

\[ 7 \frac{3}{5} = \frac{(7 \times 5) + 3}{5} = \frac{35 + 3}{5} = \frac{38}{5} \]

### Step 2: Set up the equation.
We need to find out what should be added to \(\frac{38}{5}\) to get 18. Let’s denote the unknown number as \(x\).

\[ \frac{38}{5} + x = 18 \]

### Step 3: Isolate \(x\).
To find \(x\), we can rearrange the equation:

\[ x = 18 - \frac{38}{5} \]

### Step 4: Convert 18 to a fraction with a common denominator.
To subtract \(\frac{38}{5}\) from 18, we need to express 18 as a fraction with a denominator of 5.

\[ 18 = \frac{18 \times 5}{5} = \frac{90}{5} \]

### Step 5: Perform the subtraction.
Now we can subtract the two fractions:

\[ x = \frac{90}{5} - \frac{38}{5} = \frac{90 - 38}{5} = \frac{52}{5} \]

### Step 6: Simplify if necessary.
The fraction \(\frac{52}{5}\) can also be expressed as a mixed number:

\[ \frac{52}{5} = 10 \frac{2}{5} \]

### Final Answer:
Thus, the number that should be added to \(7 \frac{3}{5}\) to get 18 is \(10 \frac{2}{5}\).

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