Question

[tex]\frac{1}{3} +(10,66:2\frac{3}{5}+1\frac{1}{5}-0,3):3

Answer 1

$\frac{1}{3} + (10\frac{66}{100} : 2\frac{3}{5} + 1\frac{1}{5} - 0,3) : 3 =$

1) $10\frac{66}{100} : 2\frac{3}{5} = \frac{1066}{100} : \frac{13}{5} = \frac{1066}{100} * \frac{5}{13} = \frac{82}{20} = 4\frac{2}{20} = 4,1$

2) $\frac{82}{20} + \frac{6}{5} = \frac{82}{20} + \frac{24}{20} = \frac{106}{20} = 5\frac{6}{20} = 5,3$

3) 5,3 - 0,3 = 5

4) 5 : 3 ≈ 1,6

5) $\frac{1}{3} + 1\frac{6}{10} = \frac{1}{3} + \frac{16}{10} = \frac{10}{30} + \frac{48}{30} = \frac{58}{30} = 1\frac{28}{30} = 1,93$

Answer 2

Let's break down the expression step by step:

Step 1: Perform the operations inside the parentheses first. $10.66:2\frac{3}{5} = 10.66:\left(2 + \frac{3}{5}\right) = 10.66:\frac{13}{5} = 10.66 \times \frac{5}{13} = 5\frac{5}{13}$.

Step 2: Now, we have the expression as $\frac{1}{3} + \left(5\frac{5}{13} + 1\frac{1}{5} - 0.3\right)$.

Step 3: Perform the addition inside the parentheses. $5\frac{5}{13} + 1\frac{1}{5} = \frac{68}{13} + \frac{6}{5}$.

To add these fractions, we need to find a common denominator, which is $13 \times 5 = 65$:

$5\frac{5}{13} + 1\frac{1}{5} = \frac{68}{13} + \frac{6}{5} = \frac{68 \times 5}{13 \times 5} + \frac{6 \times 13}{5 \times 13} = \frac{340}{65} + \frac{78}{65} = \frac{340 + 78}{65} = \frac{418}{65}$.

Step 4: Now the expression becomes $\frac{1}{3} + \frac{418}{65} - 0.3$.

Step 5: Convert $0.3$ to a fraction. $0.3 = \frac{3}{10}$.

Step 6: Find a common denominator, which is $3 \times 10 = 30$:

$\frac{1}{3} + \frac{418}{65} - 0.3 = \frac{1 \times 10}{3 \times 10} + \frac{418 \times 3}{65 \times 3} - \frac{3}{10} = \frac{10}{30} + \frac{1254}{195} - \frac{9}{30}$.

Step 7: Add the fractions: $\frac{10}{30} + \frac{1254}{195} - \frac{9}{30} = \frac{10 + 1254 - 9}{30} = \frac{1255}{30}$.

Step 8: Simplify the fraction: $\frac{1255}{30} = \frac{251}{6}$.

So, the final result of the expression is $\frac{251}{6}$ or $41\frac{5}{6}$.