Solve -(1/63*21/5-1/63*9/4+frac{1}{63}*frac{7}{6}-frac{1}{63}*frac{3}{2})

$$- ( \frac { 1 } { 63 } \times \frac { 21 } { 5 } - \frac { 1 } { 63 } \times \frac { 9 } { 4 } + \frac { 1 } { 63 } \times \frac { 7 } { 6 } - \frac { 1 } { 63 } \times \frac { 3 } { 2 } )$$

Evaluate

$$-\frac{97}{3780}\approx -0.025661376$$

Solution Steps

Multiply \frac{1}{63} times \frac{21}{5} by multiplying numerator times numerator and denominator times denominator.

$$-\left(\frac{1\times 21}{63\times 5}-\frac{1}{63}\times \frac{9}{4}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Do the multiplications in the fraction \frac{1\times 21}{63\times 5}.

$$-\left(\frac{21}{315}-\frac{1}{63}\times \frac{9}{4}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Reduce the fraction \frac{21}{315} to lowest terms by extracting and canceling out 21.

$$-\left(\frac{1}{15}-\frac{1}{63}\times \frac{9}{4}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Multiply \frac{1}{63} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\left(\frac{1}{15}-\frac{1\times 9}{63\times 4}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Do the multiplications in the fraction \frac{1\times 9}{63\times 4}.

$$-\left(\frac{1}{15}-\frac{9}{252}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Reduce the fraction \frac{9}{252} to lowest terms by extracting and canceling out 9.

$$-\left(\frac{1}{15}-\frac{1}{28}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Least common multiple of 15 and 28 is 420. Convert \frac{1}{15} and \frac{1}{28} to fractions with denominator 420.

$$-\left(\frac{28}{420}-\frac{15}{420}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Since \frac{28}{420} and \frac{15}{420} have the same denominator, subtract them by subtracting their numerators.

$$-\left(\frac{28-15}{420}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Subtract 15 from 28 to get 13.

$$-\left(\frac{13}{420}+\frac{1}{63}\times \frac{7}{6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Multiply \frac{1}{63} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\left(\frac{13}{420}+\frac{1\times 7}{63\times 6}-\frac{1}{63}\times \frac{3}{2}\right)$$

Do the multiplications in the fraction \frac{1\times 7}{63\times 6}.

$$-\left(\frac{13}{420}+\frac{7}{378}-\frac{1}{63}\times \frac{3}{2}\right)$$

Reduce the fraction \frac{7}{378} to lowest terms by extracting and canceling out 7.

$$-\left(\frac{13}{420}+\frac{1}{54}-\frac{1}{63}\times \frac{3}{2}\right)$$

Least common multiple of 420 and 54 is 3780. Convert \frac{13}{420} and \frac{1}{54} to fractions with denominator 3780.

$$-\left(\frac{117}{3780}+\frac{70}{3780}-\frac{1}{63}\times \frac{3}{2}\right)$$

Since \frac{117}{3780} and \frac{70}{3780} have the same denominator, add them by adding their numerators.

$$-\left(\frac{117+70}{3780}-\frac{1}{63}\times \frac{3}{2}\right)$$

Add 117 and 70 to get 187.

$$-\left(\frac{187}{3780}-\frac{1}{63}\times \frac{3}{2}\right)$$

Multiply \frac{1}{63} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\left(\frac{187}{3780}-\frac{1\times 3}{63\times 2}\right)$$

Do the multiplications in the fraction \frac{1\times 3}{63\times 2}.

$$-\left(\frac{187}{3780}-\frac{3}{126}\right)$$

Reduce the fraction \frac{3}{126} to lowest terms by extracting and canceling out 3.

$$-\left(\frac{187}{3780}-\frac{1}{42}\right)$$

Least common multiple of 3780 and 42 is 3780. Convert \frac{187}{3780} and \frac{1}{42} to fractions with denominator 3780.

$$-\left(\frac{187}{3780}-\frac{90}{3780}\right)$$

Since \frac{187}{3780} and \frac{90}{3780} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{187-90}{3780}$$

Subtract 90 from 187 to get 97.

$$-\frac{97}{3780}$$

Factor

$$-\frac{97}{3780} = -0.025661375661375663$$