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)
