Solve 21/13*(1/5-1/12)-7:31/2

$$2 \frac { 1 } { 13 } \cdot ( \frac { 1 } { 5 } - \frac { 1 } { 12 } ) - 7 : 3 \frac { 1 } { 2 }$$

Evaluate

$$-\frac{457}{260}\approx -1.757692308$$

Solution Steps

Multiply 2 and 13 to get 26.

$$\frac{26+1}{13}\left(\frac{1}{5}-\frac{1}{12}\right)-\frac{7}{\frac{3\times 2+1}{2}}$$

Add 26 and 1 to get 27.

$$\frac{27}{13}\left(\frac{1}{5}-\frac{1}{12}\right)-\frac{7}{\frac{3\times 2+1}{2}}$$

Least common multiple of 5 and 12 is 60. Convert \frac{1}{5} and \frac{1}{12} to fractions with denominator 60.

$$\frac{27}{13}\left(\frac{12}{60}-\frac{5}{60}\right)-\frac{7}{\frac{3\times 2+1}{2}}$$

Since \frac{12}{60} and \frac{5}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{13}\times \frac{12-5}{60}-\frac{7}{\frac{3\times 2+1}{2}}$$

Subtract 5 from 12 to get 7.

$$\frac{27}{13}\times \frac{7}{60}-\frac{7}{\frac{3\times 2+1}{2}}$$

Multiply \frac{27}{13} times \frac{7}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 7}{13\times 60}-\frac{7}{\frac{3\times 2+1}{2}}$$

Do the multiplications in the fraction \frac{27\times 7}{13\times 60}.

$$\frac{189}{780}-\frac{7}{\frac{3\times 2+1}{2}}$$

Reduce the fraction \frac{189}{780} to lowest terms by extracting and canceling out 3.

$$\frac{63}{260}-\frac{7}{\frac{3\times 2+1}{2}}$$

Divide 7 by \frac{3\times 2+1}{2} by multiplying 7 by the reciprocal of \frac{3\times 2+1}{2}.

$$\frac{63}{260}-\frac{7\times 2}{3\times 2+1}$$

Multiply 7 and 2 to get 14.

$$\frac{63}{260}-\frac{14}{3\times 2+1}$$

Multiply 3 and 2 to get 6.

$$\frac{63}{260}-\frac{14}{6+1}$$

Add 6 and 1 to get 7.

$$\frac{63}{260}-\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$\frac{63}{260}-2$$

Convert 2 to fraction \frac{520}{260}.

$$\frac{63}{260}-\frac{520}{260}$$

Since \frac{63}{260} and \frac{520}{260} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-520}{260}$$

Subtract 520 from 63 to get -457.

$$-\frac{457}{260}$$

Factor

$$-\frac{457}{260} = -1\frac{197}{260} = -1.7576923076923077$$