What should be added to `(7)/(12)` to get `(-4)/(15)`?

Options

A. `(17)/(20)`
B. `(-17)/(20)`
C. `(7)/(20)`
D. `(-7)/(20)`

Answer

To solve the problem of what should be added to \(\frac{7}{12}\) to get \(-\frac{4}{15}\), we can follow these steps:

### Step 1: Set up the equation
Let \(x\) be the number that we need to find. According to the problem, we can set up the equation:
\[ \frac{7}{12} + x = -\frac{4}{15} \]

### Step 2: Isolate \(x\)
To find \(x\), we need to isolate it on one side of the equation. We can do this by subtracting \(\frac{7}{12}\) from both sides:
\[ x = -\frac{4}{15} - \frac{7}{12} \]

### Step 3: Find a common denominator
To subtract the fractions, we need a common denominator. The denominators are 15 and 12. The least common multiple (LCM) of 15 and 12 is 60.

### Step 4: Convert the fractions
Now, we convert both fractions to have a denominator of 60:
\[ -\frac{4}{15} = -\frac{4 \times 4}{15 \times 4} = -\frac{16}{60} \]
\[ \frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60} \]

### Step 5: Substitute back into the equation
Now we can substitute these values back into the equation for \(x\):
\[ x = -\frac{16}{60} - \frac{35}{60} \]

### Step 6: Combine the fractions
Now we can combine the fractions:
\[ x = \frac{-16 - 35}{60} = \frac{-51}{60} \]

### Step 7: Final answer
Thus, the value of \(x\) is:
\[ x = -\frac{51}{60} \]

### Summary
The number that should be added to \(\frac{7}{12}\) to get \(-\frac{4}{15}\) is \(-\frac{51}{60}\).

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