Solve 4/9div7/3+1/42-31/42

$$\frac{ 4 }{ 9 } \div \frac{ 7 }{ 3 } + \frac{ 1 }{ 42 } - \frac{ 31 }{ 42 }$$

Evaluate

$$-\frac{11}{21}\approx -0.523809524$$

Solution Steps

Divide \frac{4}{9} by \frac{7}{3} by multiplying \frac{4}{9} by the reciprocal of \frac{7}{3}.

$$\frac{4}{9}\times \frac{3}{7}+\frac{1}{42}-\frac{31}{42}$$

Multiply \frac{4}{9} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 3}{9\times 7}+\frac{1}{42}-\frac{31}{42}$$

Do the multiplications in the fraction \frac{4\times 3}{9\times 7}.

$$\frac{12}{63}+\frac{1}{42}-\frac{31}{42}$$

Reduce the fraction \frac{12}{63} to lowest terms by extracting and canceling out 3.

$$\frac{4}{21}+\frac{1}{42}-\frac{31}{42}$$

Least common multiple of 21 and 42 is 42. Convert \frac{4}{21} and \frac{1}{42} to fractions with denominator 42.

$$\frac{8}{42}+\frac{1}{42}-\frac{31}{42}$$

Since \frac{8}{42} and \frac{1}{42} have the same denominator, add them by adding their numerators.

$$\frac{8+1}{42}-\frac{31}{42}$$

Add 8 and 1 to get 9.

$$\frac{9}{42}-\frac{31}{42}$$

Since \frac{9}{42} and \frac{31}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-31}{42}$$

Subtract 31 from 9 to get -22.

$$\frac{-22}{42}$$

Reduce the fraction \frac{-22}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{21}$$

Factor

$$-\frac{11}{21} = -0.5238095238095238$$