Solve (2.5-7.5/5)*0.5/(2-1.8)div0.4+(65/3-3frac{3/14)*5frac{5}{6}}{(21-1.25)div2.5}

$$\frac{ (2.5- \frac{ 7.5 }{ 5 } ) \times 0.5 }{ (2-1.8) \div 0.4 } + \frac{ (6 \frac{ 5 }{ 3 } -3 \frac{ 3 }{ 14 } ) \times 5 \frac{ 5 }{ 6 } }{ (21-1.25) \div 2.5 }$$

Evaluate

$$\frac{6097}{1422}\approx 4.287623066$$

Solution Steps

Expand \frac{7.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{\left(2.5-\frac{75}{50}\right)\times 0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Reduce the fraction \frac{75}{50} to lowest terms by extracting and canceling out 25.

$$\frac{\left(2.5-\frac{3}{2}\right)\times 0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\left(\frac{5}{2}-\frac{3}{2}\right)\times 0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Since \frac{5}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-3}{2}\times 0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Subtract 3 from 5 to get 2.

$$\frac{\frac{2}{2}\times 0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Divide 2 by 2 to get 1.

$$\frac{1\times 0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Multiply 1 and 0.5 to get 0.5.

$$\frac{0.5}{\frac{2-1.8}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Subtract 1.8 from 2 to get 0.2.

$$\frac{0.5}{\frac{0.2}{0.4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Expand \frac{0.2}{0.4} by multiplying both numerator and the denominator by 10.

$$\frac{0.5}{\frac{2}{4}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{0.5}{\frac{1}{2}}+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Divide 0.5 by \frac{1}{2} to get 1.

$$1+\frac{\left(\frac{6\times 3+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Multiply 6 and 3 to get 18.

$$1+\frac{\left(\frac{18+5}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Add 18 and 5 to get 23.

$$1+\frac{\left(\frac{23}{3}-\frac{3\times 14+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Multiply 3 and 14 to get 42.

$$1+\frac{\left(\frac{23}{3}-\frac{42+3}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Add 42 and 3 to get 45.

$$1+\frac{\left(\frac{23}{3}-\frac{45}{14}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Least common multiple of 3 and 14 is 42. Convert \frac{23}{3} and \frac{45}{14} to fractions with denominator 42.

$$1+\frac{\left(\frac{322}{42}-\frac{135}{42}\right)\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Since \frac{322}{42} and \frac{135}{42} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{\frac{322-135}{42}\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Subtract 135 from 322 to get 187.

$$1+\frac{\frac{187}{42}\times \frac{5\times 6+5}{6}}{\frac{21-1.25}{2.5}}$$

Multiply 5 and 6 to get 30.

$$1+\frac{\frac{187}{42}\times \frac{30+5}{6}}{\frac{21-1.25}{2.5}}$$

Add 30 and 5 to get 35.

$$1+\frac{\frac{187}{42}\times \frac{35}{6}}{\frac{21-1.25}{2.5}}$$

Multiply \frac{187}{42} times \frac{35}{6} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{\frac{187\times 35}{42\times 6}}{\frac{21-1.25}{2.5}}$$

Do the multiplications in the fraction \frac{187\times 35}{42\times 6}.

$$1+\frac{\frac{6545}{252}}{\frac{21-1.25}{2.5}}$$

Reduce the fraction \frac{6545}{252} to lowest terms by extracting and canceling out 7.

$$1+\frac{\frac{935}{36}}{\frac{21-1.25}{2.5}}$$

Subtract 1.25 from 21 to get 19.75.

$$1+\frac{\frac{935}{36}}{\frac{19.75}{2.5}}$$

Expand \frac{19.75}{2.5} by multiplying both numerator and the denominator by 100.

$$1+\frac{\frac{935}{36}}{\frac{1975}{250}}$$

Reduce the fraction \frac{1975}{250} to lowest terms by extracting and canceling out 25.

$$1+\frac{\frac{935}{36}}{\frac{79}{10}}$$

Divide \frac{935}{36} by \frac{79}{10} by multiplying \frac{935}{36} by the reciprocal of \frac{79}{10}.

$$1+\frac{935}{36}\times \frac{10}{79}$$

Multiply \frac{935}{36} times \frac{10}{79} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{935\times 10}{36\times 79}$$

Do the multiplications in the fraction \frac{935\times 10}{36\times 79}.

$$1+\frac{9350}{2844}$$

Reduce the fraction \frac{9350}{2844} to lowest terms by extracting and canceling out 2.

$$1+\frac{4675}{1422}$$

Convert 1 to fraction \frac{1422}{1422}.

$$\frac{1422}{1422}+\frac{4675}{1422}$$

Since \frac{1422}{1422} and \frac{4675}{1422} have the same denominator, add them by adding their numerators.

$$\frac{1422+4675}{1422}$$

Add 1422 and 4675 to get 6097.

$$\frac{6097}{1422}$$

Factor

$$\frac{7 \cdot 13 \cdot 67}{2 \cdot 79 \cdot 3 ^ {2}} = 4\frac{409}{1422} = 4.287623066104079$$