Subtract, answer as a fraction in simplest form.

Question

7/12 - 2/5
[__]/[__]

Answer 1

To subtract the fractions \( \frac{7}{12} - \frac{2}{5} \), we first need a common denominator.

The denominators are 12 and 5. The least common multiple (LCM) of 12 and 5 is 60.

Next, we convert each fraction to have the denominator of 60:

1. For \( \frac{7}{12} \): \[ \frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60} \]

2. For \( \frac{2}{5} \): \[ \frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60} \]

Now we can subtract the two fractions: \[ \frac{35}{60} - \frac{24}{60} = \frac{35 - 24}{60} = \frac{11}{60} \]

Now, we will check if \( \frac{11}{60} \) is in simplest form. The numerator 11 is a prime number, and it does not divide 60. Therefore, \( \frac{11}{60} \) is already in simplest form.

Thus, the final answer is \[ \frac{11}{60} \]

So, the answer is: \[ [11]/[60] \]