Solve (61/2-7)(61/3-7)*(67/4-7)*(64/5-7)+6frac{7}{6}-7

$$( 6 \frac { 1 } { 2 } - 7 ) ( 6 \frac { 1 } { 3 } - 7 ) \cdot ( 6 \frac { 7 } { 4 } - 7 ) \cdot ( 6 \frac { 4 } { 5 } - 7 ) + 6 \frac { 7 } { 6 } - 7$$

Evaluate

$$\frac{7}{60}\approx 0.116666667$$

Solution Steps

Multiply 6 and 2 to get 12.

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

Add 12 and 1 to get 13.

$$\left(\frac{13}{2}-7\right)\left(\frac{6\times 3+1}{3}-7\right)\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Convert 7 to fraction \frac{14}{2}.

$$\left(\frac{13}{2}-\frac{14}{2}\right)\left(\frac{6\times 3+1}{3}-7\right)\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Since \frac{13}{2} and \frac{14}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-14}{2}\left(\frac{6\times 3+1}{3}-7\right)\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Subtract 14 from 13 to get -1.

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

Multiply 6 and 3 to get 18.

$$-\frac{1}{2}\left(\frac{18+1}{3}-7\right)\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Add 18 and 1 to get 19.

$$-\frac{1}{2}\left(\frac{19}{3}-7\right)\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Convert 7 to fraction \frac{21}{3}.

$$-\frac{1}{2}\left(\frac{19}{3}-\frac{21}{3}\right)\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Since \frac{19}{3} and \frac{21}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}\times \frac{19-21}{3}\left(\frac{6\times 4+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Subtract 21 from 19 to get -2.

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

Multiply -\frac{1}{2} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-\left(-2\right)}{2\times 3}.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Multiply 6 and 4 to get 24.

$$\frac{1}{3}\left(\frac{24+7}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Add 24 and 7 to get 31.

$$\frac{1}{3}\left(\frac{31}{4}-7\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Convert 7 to fraction \frac{28}{4}.

$$\frac{1}{3}\left(\frac{31}{4}-\frac{28}{4}\right)\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Since \frac{31}{4} and \frac{28}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{31-28}{4}\left(\frac{6\times 5+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Subtract 28 from 31 to get 3.

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

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 6 and 5 to get 30.

$$\frac{1}{4}\left(\frac{30+4}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Add 30 and 4 to get 34.

$$\frac{1}{4}\left(\frac{34}{5}-7\right)+\frac{6\times 6+7}{6}-7$$

Convert 7 to fraction \frac{35}{5}.

$$\frac{1}{4}\left(\frac{34}{5}-\frac{35}{5}\right)+\frac{6\times 6+7}{6}-7$$

Since \frac{34}{5} and \frac{35}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}\times \frac{34-35}{5}+\frac{6\times 6+7}{6}-7$$

Subtract 35 from 34 to get -1.

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

Multiply \frac{1}{4} times -\frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 5}.

$$\frac{-1}{20}+\frac{6\times 6+7}{6}-7$$

Fraction \frac{-1}{20} can be rewritten as -\frac{1}{20} by extracting the negative sign.

$$-\frac{1}{20}+\frac{6\times 6+7}{6}-7$$

Multiply 6 and 6 to get 36.

$$-\frac{1}{20}+\frac{36+7}{6}-7$$

Add 36 and 7 to get 43.

$$-\frac{1}{20}+\frac{43}{6}-7$$

Least common multiple of 20 and 6 is 60. Convert -\frac{1}{20} and \frac{43}{6} to fractions with denominator 60.

$$-\frac{3}{60}+\frac{430}{60}-7$$

Since -\frac{3}{60} and \frac{430}{60} have the same denominator, add them by adding their numerators.

$$\frac{-3+430}{60}-7$$

Add -3 and 430 to get 427.

$$\frac{427}{60}-7$$

Convert 7 to fraction \frac{420}{60}.

$$\frac{427}{60}-\frac{420}{60}$$

Since \frac{427}{60} and \frac{420}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{427-420}{60}$$

Subtract 420 from 427 to get 7.

$$\frac{7}{60}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3 \cdot 5} = 0.11666666666666667$$