Solve 8/49div[9/8-(1/8+3/7)]

$$\frac { 8 } { 49 } \div [ \frac { 9 } { 8 } - ( \frac { 1 } { 8 } + \frac { 3 } { 7 } ) ]$$

Evaluate

$$\frac{2}{7}\approx 0.285714286$$

Solution Steps

Least common multiple of 8 and 7 is 56. Convert \frac{1}{8} and \frac{3}{7} to fractions with denominator 56.

$$\frac{\frac{8}{49}}{\frac{9}{8}-\left(\frac{7}{56}+\frac{24}{56}\right)}$$

Since \frac{7}{56} and \frac{24}{56} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{49}}{\frac{9}{8}-\frac{7+24}{56}}$$

Add 7 and 24 to get 31.

$$\frac{\frac{8}{49}}{\frac{9}{8}-\frac{31}{56}}$$

Least common multiple of 8 and 56 is 56. Convert \frac{9}{8} and \frac{31}{56} to fractions with denominator 56.

$$\frac{\frac{8}{49}}{\frac{63}{56}-\frac{31}{56}}$$

Since \frac{63}{56} and \frac{31}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{49}}{\frac{63-31}{56}}$$

Subtract 31 from 63 to get 32.

$$\frac{\frac{8}{49}}{\frac{32}{56}}$$

Reduce the fraction \frac{32}{56} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{8}{49}}{\frac{4}{7}}$$

Divide \frac{8}{49} by \frac{4}{7} by multiplying \frac{8}{49} by the reciprocal of \frac{4}{7}.

$$\frac{8}{49}\times \frac{7}{4}$$

Multiply \frac{8}{49} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 7}{49\times 4}$$

Do the multiplications in the fraction \frac{8\times 7}{49\times 4}.

$$\frac{56}{196}$$

Reduce the fraction \frac{56}{196} to lowest terms by extracting and canceling out 28.

$$\frac{2}{7}$$

Factor

$$\frac{2}{7} = 0.2857142857142857$$