11/16-5/12

To subtract the fractions \( \frac{11}{16} - \frac{5}{12} \), we first need to find a common denominator. The least common multiple (LCM) of 16 and 12 can be found as follows:

• The prime factorization of 16 is \( 2^4 \).
• The prime factorization of 12 is \( 2^2 \times 3 \).

The LCM takes the highest power of each prime:

• For 2, the highest power is \( 2^4 \).
• For 3, the highest power is \( 3^1 \).

So, \( \text{LCM}(16, 12) = 2^4 \times 3^1 = 16 \times 3 = 48 \).

Now, we can rewrite both fractions with the common denominator of 48:

1. Convert \( \frac{11}{16} \) to a fraction with a denominator of 48:

\[ \frac{11}{16} = \frac{11 \times 3}{16 \times 3} = \frac{33}{48} \]

2. Convert \( \frac{5}{12} \) to a fraction with a denominator of 48:

\[ \frac{5}{12} = \frac{5 \times 4}{12 \times 4} = \frac{20}{48} \]

Now we can subtract the two fractions:

\[ \frac{33}{48} - \frac{20}{48} = \frac{33 - 20}{48} = \frac{13}{48} \]

Thus, the result of \( \frac{11}{16} - \frac{5}{12} \) is \( \frac{13}{48} \).