15/56+11/84

To add the fractions \( \frac{15}{56} \) and \( \frac{11}{84} \), we need to find a common denominator.

The least common multiple (LCM) of 56 and 84 can be found as follows:

• The prime factorization of 56 is \( 2^3 \times 7 \).
• The prime factorization of 84 is \( 2^2 \times 3 \times 7 \).

The LCM will take the highest power of each prime factor:

• For \( 2 \): \( 2^3 \)
• For \( 3 \): \( 3^1 \)
• For \( 7 \): \( 7^1 \)

Thus, the LCM is: \[ 2^3 \times 3^1 \times 7^1 = 8 \times 3 \times 7 = 168 \]

Now we convert each fraction to have a denominator of 168:

1. For \( \frac{15}{56} \): \[ \frac{15}{56} = \frac{15 \times 3}{56 \times 3} = \frac{45}{168} \]

2. For \( \frac{11}{84} \): \[ \frac{11}{84} = \frac{11 \times 2}{84 \times 2} = \frac{22}{168} \]

Now we can add the two fractions: \[ \frac{45}{168} + \frac{22}{168} = \frac{45 + 22}{168} = \frac{67}{168} \]

So, \( \frac{15}{56} + \frac{11}{84} = \frac{67}{168} \).