Solve 31/2-(1.25-21/3)(2)31/7div34/7*frac{5}{12}

$$3 \frac { 1 } { 2 } - ( 1.25 - 2 \frac { 1 } { 3 } ) ( 2 ) 3 \frac { 1 } { 7 } \div 3 \frac { 4 } { 7 } \times \frac { 5 } { 12 }$$

Evaluate

$$\frac{773}{180}\approx 4.294444444$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-\frac{\left(1.25-\frac{2\times 3+1}{3}\right)\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\frac{\left(1.25-\frac{2\times 3+1}{3}\right)\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{2}-\frac{\left(1.25-\frac{6+1}{3}\right)\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\frac{\left(1.25-\frac{7}{3}\right)\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Convert decimal number 1.25 to fraction \frac{125}{100}. Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{7}{2}-\frac{\left(\frac{5}{4}-\frac{7}{3}\right)\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{7}{2}-\frac{\left(\frac{15}{12}-\frac{28}{12}\right)\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Since \frac{15}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}-\frac{\frac{15-28}{12}\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Subtract 28 from 15 to get -13.

$$\frac{7}{2}-\frac{-\frac{13}{12}\times 2\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Express -\frac{13}{12}\times 2 as a single fraction.

$$\frac{7}{2}-\frac{\frac{-13\times 2}{12}\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Multiply -13 and 2 to get -26.

$$\frac{7}{2}-\frac{\frac{-26}{12}\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Reduce the fraction \frac{-26}{12} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}-\frac{-\frac{13}{6}\times \frac{3\times 7+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Multiply 3 and 7 to get 21.

$$\frac{7}{2}-\frac{-\frac{13}{6}\times \frac{21+1}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Add 21 and 1 to get 22.

$$\frac{7}{2}-\frac{-\frac{13}{6}\times \frac{22}{7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Multiply -\frac{13}{6} times \frac{22}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}-\frac{\frac{-13\times 22}{6\times 7}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Do the multiplications in the fraction \frac{-13\times 22}{6\times 7}.

$$\frac{7}{2}-\frac{\frac{-286}{42}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Reduce the fraction \frac{-286}{42} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}-\frac{-\frac{143}{21}}{\frac{3\times 7+4}{7}}\times \frac{5}{12}$$

Multiply 3 and 7 to get 21.

$$\frac{7}{2}-\frac{-\frac{143}{21}}{\frac{21+4}{7}}\times \frac{5}{12}$$

Add 21 and 4 to get 25.

$$\frac{7}{2}-\frac{-\frac{143}{21}}{\frac{25}{7}}\times \frac{5}{12}$$

Divide -\frac{143}{21} by \frac{25}{7} by multiplying -\frac{143}{21} by the reciprocal of \frac{25}{7}.

$$\frac{7}{2}-\left(-\frac{143}{21}\times \frac{7}{25}\times \frac{5}{12}\right)$$

Multiply -\frac{143}{21} times \frac{7}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}-\frac{-143\times 7}{21\times 25}\times \frac{5}{12}$$

Do the multiplications in the fraction \frac{-143\times 7}{21\times 25}.

$$\frac{7}{2}-\frac{-1001}{525}\times \frac{5}{12}$$

Reduce the fraction \frac{-1001}{525} to lowest terms by extracting and canceling out 7.

$$\frac{7}{2}-\left(-\frac{143}{75}\times \frac{5}{12}\right)$$

Multiply -\frac{143}{75} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}-\frac{-143\times 5}{75\times 12}$$

Do the multiplications in the fraction \frac{-143\times 5}{75\times 12}.

$$\frac{7}{2}-\frac{-715}{900}$$

Reduce the fraction \frac{-715}{900} to lowest terms by extracting and canceling out 5.

$$\frac{7}{2}-\left(-\frac{143}{180}\right)$$

The opposite of -\frac{143}{180} is \frac{143}{180}.

$$\frac{7}{2}+\frac{143}{180}$$

Least common multiple of 2 and 180 is 180. Convert \frac{7}{2} and \frac{143}{180} to fractions with denominator 180.

$$\frac{630}{180}+\frac{143}{180}$$

Since \frac{630}{180} and \frac{143}{180} have the same denominator, add them by adding their numerators.

$$\frac{630+143}{180}$$

Add 630 and 143 to get 773.

$$\frac{773}{180}$$

Factor

$$\frac{773}{5 \cdot 2 ^ {2} \cdot 3 ^ {2}} = 4\frac{53}{180} = 4.294444444444444$$