Solve 54/9*15/7/2frac{5{7}-9/14}

$$\frac { 5 \frac { 4 } { 9 } \times \frac { 15 } { 7 } } { 2 \frac { 5 } { 7 } - \frac { 9 } { 14 } }$$

Evaluate

$$\frac{490}{87}\approx 5.632183908$$

Solution Steps

Multiply 5 and 9 to get 45.

$$\frac{\frac{45+4}{9}\times \frac{15}{7}}{\frac{2\times 7+5}{7}-\frac{9}{14}}$$

Add 45 and 4 to get 49.

$$\frac{\frac{49}{9}\times \frac{15}{7}}{\frac{2\times 7+5}{7}-\frac{9}{14}}$$

Multiply \frac{49}{9} times \frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{49\times 15}{9\times 7}}{\frac{2\times 7+5}{7}-\frac{9}{14}}$$

Do the multiplications in the fraction \frac{49\times 15}{9\times 7}.

$$\frac{\frac{735}{63}}{\frac{2\times 7+5}{7}-\frac{9}{14}}$$

Reduce the fraction \frac{735}{63} to lowest terms by extracting and canceling out 21.

$$\frac{\frac{35}{3}}{\frac{2\times 7+5}{7}-\frac{9}{14}}$$

Multiply 2 and 7 to get 14.

$$\frac{\frac{35}{3}}{\frac{14+5}{7}-\frac{9}{14}}$$

Add 14 and 5 to get 19.

$$\frac{\frac{35}{3}}{\frac{19}{7}-\frac{9}{14}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{19}{7} and \frac{9}{14} to fractions with denominator 14.

$$\frac{\frac{35}{3}}{\frac{38}{14}-\frac{9}{14}}$$

Since \frac{38}{14} and \frac{9}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35}{3}}{\frac{38-9}{14}}$$

Subtract 9 from 38 to get 29.

$$\frac{\frac{35}{3}}{\frac{29}{14}}$$

Divide \frac{35}{3} by \frac{29}{14} by multiplying \frac{35}{3} by the reciprocal of \frac{29}{14}.

$$\frac{35}{3}\times \frac{14}{29}$$

Multiply \frac{35}{3} times \frac{14}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 14}{3\times 29}$$

Do the multiplications in the fraction \frac{35\times 14}{3\times 29}.

$$\frac{490}{87}$$

Factor

$$\frac{2 \cdot 5 \cdot 7 ^ {2}}{3 \cdot 29} = 5\frac{55}{87} = 5.632183908045977$$