Solve 2/3*5/7+1/4*2/7-frac{7}{3}*frac{1}{4}=

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

Evaluate

$$-\frac{1}{28}\approx -0.035714286$$

Solution Steps

Multiply \frac{2}{3} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 5}{3\times 7}.

$$\frac{10}{21}+\frac{1}{4}\times \frac{2}{7}-\frac{7}{3}\times \frac{1}{4}$$

Multiply \frac{1}{4} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{21}+\frac{1\times 2}{4\times 7}-\frac{7}{3}\times \frac{1}{4}$$

Do the multiplications in the fraction \frac{1\times 2}{4\times 7}.

$$\frac{10}{21}+\frac{2}{28}-\frac{7}{3}\times \frac{1}{4}$$

Reduce the fraction \frac{2}{28} to lowest terms by extracting and canceling out 2.

$$\frac{10}{21}+\frac{1}{14}-\frac{7}{3}\times \frac{1}{4}$$

Least common multiple of 21 and 14 is 42. Convert \frac{10}{21} and \frac{1}{14} to fractions with denominator 42.

$$\frac{20}{42}+\frac{3}{42}-\frac{7}{3}\times \frac{1}{4}$$

Since \frac{20}{42} and \frac{3}{42} have the same denominator, add them by adding their numerators.

$$\frac{20+3}{42}-\frac{7}{3}\times \frac{1}{4}$$

Add 20 and 3 to get 23.

$$\frac{23}{42}-\frac{7}{3}\times \frac{1}{4}$$

Multiply \frac{7}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23}{42}-\frac{7\times 1}{3\times 4}$$

Do the multiplications in the fraction \frac{7\times 1}{3\times 4}.

$$\frac{23}{42}-\frac{7}{12}$$

Least common multiple of 42 and 12 is 84. Convert \frac{23}{42} and \frac{7}{12} to fractions with denominator 84.

$$\frac{46}{84}-\frac{49}{84}$$

Since \frac{46}{84} and \frac{49}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46-49}{84}$$

Subtract 49 from 46 to get -3.

$$\frac{-3}{84}$$

Reduce the fraction \frac{-3}{84} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{28}$$

Factor

$$-\frac{1}{28} = -0.03571428571428571$$