The sum of two fractions is `3/5` If one of the fractions is `7/12` then find the difference of two fractions.

Options

A. `(17)/(30)`
B. `(33)/(60)`
C. `(15)/(17)`
D. `(5)/(12)`

Answer

To solve the problem step by step, we need to find the difference between two fractions given that their sum is \( \frac{3}{5} \) and one of the fractions is \( \frac{7}{12} \).

### Step 1: Set up the equation
Let the unknown fraction be \( x \). According to the problem, we have:
\[ x + \frac{7}{12} = \frac{3}{5} \]

### Step 2: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{3}{5} - \frac{7}{12} \]

### Step 3: Find a common denominator
To subtract the fractions, we need a common denominator. The denominators are 5 and 12. The least common multiple (LCM) of 5 and 12 is 60.

### Step 4: Convert the fractions
Now, we convert each fraction to have the common denominator of 60:
- For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 12}{5 \times 12} = \frac{36}{60} \]
- For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60} \]

### Step 5: Perform the subtraction
Now we can subtract the two fractions:
\[ x = \frac{36}{60} - \frac{35}{60} = \frac{36 - 35}{60} = \frac{1}{60} \]

### Step 6: Find the difference between the two fractions
Now we need to find the difference between \( \frac{7}{12} \) and \( \frac{1}{60} \):
\[ \text{Difference} = \frac{7}{12} - \frac{1}{60} \]

### Step 7: Convert to a common denominator
Again, we will use 60 as the common denominator:
- For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60} \]

### Step 8: Perform the subtraction
Now we can subtract:
\[ \text{Difference} = \frac{35}{60} - \frac{1}{60} = \frac{35 - 1}{60} = \frac{34}{60} \]

### Step 9: Simplify the fraction
Now we simplify \( \frac{34}{60} \):
\[ \frac{34 \div 2}{60 \div 2} = \frac{17}{30} \]

### Final Answer
The difference of the two fractions is:
\[ \frac{17}{30} \]

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