Solve (5/7+2/3)*(5-3/4)

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

Evaluate

$$\frac{493}{84}\approx 5.869047619$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{5}{7} and \frac{2}{3} to fractions with denominator 21.

$$\left(\frac{15}{21}+\frac{14}{21}\right)\left(5-\frac{3}{4}\right)$$

Since \frac{15}{21} and \frac{14}{21} have the same denominator, add them by adding their numerators.

$$\frac{15+14}{21}\left(5-\frac{3}{4}\right)$$

Add 15 and 14 to get 29.

$$\frac{29}{21}\left(5-\frac{3}{4}\right)$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{29}{21}\left(\frac{20}{4}-\frac{3}{4}\right)$$

Since \frac{20}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29}{21}\times \frac{20-3}{4}$$

Subtract 3 from 20 to get 17.

$$\frac{29}{21}\times \frac{17}{4}$$

Multiply \frac{29}{21} times \frac{17}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 17}{21\times 4}$$

Do the multiplications in the fraction \frac{29\times 17}{21\times 4}.

$$\frac{493}{84}$$

Factor

$$\frac{17 \cdot 29}{2 ^ {2} \cdot 3 \cdot 7} = 5\frac{73}{84} = 5.869047619047619$$