5/16+7/20

To add the fractions \( \frac{5}{16} \) and \( \frac{7}{20} \), you need to find a common denominator.

The least common multiple (LCM) of 16 and 20 can be calculated as follows:

• The prime factorization of 16 is \( 2^4 \).
• The prime factorization of 20 is \( 2^2 \times 5 \).

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

• For 2, the highest power is \( 2^4 \).
• For 5, the highest power is \( 5^1 \).

So, the LCM of 16 and 20 is \( 2^4 \times 5^1 = 16 \times 5 = 80 \).

Now, convert each fraction to have a denominator of 80:

1. For \( \frac{5}{16} \): \[ \frac{5}{16} = \frac{5 \times 5}{16 \times 5} = \frac{25}{80} \]

2. For \( \frac{7}{20} \): \[ \frac{7}{20} = \frac{7 \times 4}{20 \times 4} = \frac{28}{80} \]

Now add the two fractions: \[ \frac{25}{80} + \frac{28}{80} = \frac{25 + 28}{80} = \frac{53}{80} \]

So, \( \frac{5}{16} + \frac{7}{20} = \frac{53}{80} \).