Evaluate the expression shown below and write ur answer as a fraction in simplest form. (8/5 - 11/10) • 5/7

Answer 1

To evaluate the expression \((\frac{8}{5} - \frac{11}{10}) \cdot \frac{5}{7}\), let's follow the steps:

1. Subtract the fractions inside the parentheses: \(\frac{8}{5} - \frac{11}{10}\)

   To subtract these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10. We can convert \(\frac{8}{5}\) to have a denominator of 10:

   \[ \frac{8}{5} = \frac{8 \cdot 2}{5 \cdot 2} = \frac{16}{10} \]

   Now we can perform the subtraction:

   \[ \frac{16}{10} - \frac{11}{10} = \frac{16 - 11}{10} = \frac{5}{10} \]

   We can simplify \(\frac{5}{10}\):

   \[ \frac{5}{10} = \frac{1}{2} \]

2. Multiply by \(\frac{5}{7}\): Now we take the result \(\frac{1}{2}\) and multiply it by \(\frac{5}{7}\):

   \[ \frac{1}{2} \cdot \frac{5}{7} = \frac{1 \cdot 5}{2 \cdot 7} = \frac{5}{14} \]

Thus, the evaluated expression \((\frac{8}{5} - \frac{11}{10}) \cdot \frac{5}{7}\) in simplest form is

\[ \boxed{\frac{5}{14}} \]