Question

(9- 3 4/5 ) • ( 1 5/6 + 1/9) - 2/3

Answer 1

$(9 - 3 \frac{4}{5} ) \times (1 \frac{5}{6} + \frac{1}{9} ) - \frac{2}{3} = 13 \times \frac{7}{9} - \frac{2}{3} = \frac{85}{9}$

Answer 2

$(9 - 3 \frac{4}{5} ) \times (1 \frac{5}{6} + \frac{1}{9} ) - \frac{2}{3} = \\ \\ = (8 \frac{5}{5} - 3 \frac{4}{5} ) \times (1 \frac{15}{18} + \frac{2}{18} ) - \frac{2}{3} = \\ \\ = 5 \frac{1}{5} \times 1 \frac{17}{18} - \frac{2}{3} = \frac{26 \times 35}{5 \times 18} - \frac{2}{3} = \\ \\ = \frac{91}{9} - \frac{2}{3} = \frac{91}{9} - \frac{6}{9} = \frac{85}{9} = 9 \frac{4}{9}$

Answer 3

Let's break down the expression step by step:

1. Evaluate the expression inside the parentheses: (9 - 3 4/5) • (1 5/6 + 1/9) - 2/3

   First, let's simplify the subtraction inside the first parentheses: 9 - 3 4/5 = 8 1/5

   Next, let's simplify the addition inside the second parentheses: 1 5/6 + 1/9 = (9/6 + 1/9) = (27/18 + 2/18) = 29/18

2. Now, let's substitute the simplified values back into the expression: (8 1/5) • (29/18) - 2/3

3. To multiply mixed numbers, convert them to improper fractions: 8 1/5 = (8 * 5 + 1) / 5 = 41/5

4. Perform the multiplication: (41/5) • (29/18) - 2/3

   To multiply fractions, multiply the numerators together and the denominators together: (41/5) • (29/18) = (41 * 29) / (5 * 18) = 1189/90

5. Subtract 2/3 from the result: (1189/90) - 2/3

   To subtract fractions, we need a common denominator, which is the least common multiple of 90 and 3, which is 90. Convert 2/3 to have a denominator of 90: 2/3 = (2 * 30) / (3 * 30) = 60/90

   Now we can perform the subtraction: (1189/90) - (60/90) = (1189 - 60) / 90 = 1129/90

6. Simplify the fraction: 1129/90 = (1129/1) / (90/1) = 1129/90 = 125 19/90

Therefore, the final result is 125 19/90.