2 9 + 4/15 - 3/20

To solve the expression \( 2 \frac{9}{15} - \frac{3}{20} \), we first need to convert the mixed number into an improper fraction.

1. Convert the mixed number \( 2 \frac{9}{15} \): \[ 2 \frac{9}{15} = 2 + \frac{9}{15} = \frac{2 \times 15 + 9}{15} = \frac{30 + 9}{15} = \frac{39}{15} \]

Now our expression looks like this: \[ \frac{39}{15} - \frac{3}{20} \]

2. To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 15 and 20 is 60.

3. Convert both fractions to have the common denominator of 60:

   • For \( \frac{39}{15} \): \[ \frac{39}{15} = \frac{39 \times 4}{15 \times 4} = \frac{156}{60} \]
   • For \( \frac{3}{20} \): \[ \frac{3}{20} = \frac{3 \times 3}{20 \times 3} = \frac{9}{60} \]

4. Now we can subtract: \[ \frac{156}{60} - \frac{9}{60} = \frac{156 - 9}{60} = \frac{147}{60} \]

5. Finally, simplify \( \frac{147}{60} \):

   • The greatest common divisor (GCD) of 147 and 60 is 3. \[ \frac{147 \div 3}{60 \div 3} = \frac{49}{20} \]

Thus, the final simplified result of \( 2 \frac{9}{15} - \frac{3}{20} \) is: \[ \frac{49}{20} \] or as a mixed number: \[ 2 \frac{9}{20} \]