6 2/5+3/4*4/5

To solve this equation, we need to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Given expression: \(6 \frac{2}{5} + \frac{3}{4} \times \frac{4}{5}\)

First, let's convert the mixed number \(6 \frac{2}{5}\) to an improper fraction: \(6 \frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{32}{5}\)

Substitute this back into the expression: \(\frac{32}{5} + \frac{3}{4} \times \frac{4}{5}\)

Next, multiply the fractions \(\frac{3}{4} \times \frac{4}{5}\): \(\frac{3}{4} \times \frac{4}{5} = \frac{3 \times 4}{4 \times 5} = \frac{12}{20}\)

Now, the expression becomes: \(\frac{32}{5} + \frac{12}{20}\)

To add these fractions, we need to find a common denominator. The common denominator for 5 and 20 is 20.

Rewrite \(\frac{32}{5}\) in terms of the common denominator 20: \(\frac{32}{5} = \frac{32 \times 4}{5 \times 4} = \frac{128}{20}\)

Now the expression becomes: \(\frac{128}{20} + \frac{12}{20}\)

Add the fractions with the common denominator 20: \(\frac{128+12}{20} = \frac{140}{20}\)

Finally, simplify the fraction: \(\frac{140}{20} = \frac{7 \times 20}{1 \times 20} = 7\)

So, \(6 \frac{2}{5} + \frac{3}{4} \times \frac{4}{5} = 7\)