Solve 5/2(20/9)-5/6(20/9)

$$\frac{ 5 }{ 2 } ( \frac{ 20 }{ 9 } )- \frac{ 5 }{ 6 } ( \frac{ 20 }{ 9 } )$$

Evaluate

$$\frac{100}{27}\approx 3.703703704$$

Solution Steps

Multiply \frac{5}{2} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 20}{2\times 9}-\frac{5}{6}\times \frac{20}{9}$$

Do the multiplications in the fraction \frac{5\times 20}{2\times 9}.

$$\frac{100}{18}-\frac{5}{6}\times \frac{20}{9}$$

Reduce the fraction \frac{100}{18} to lowest terms by extracting and canceling out 2.

$$\frac{50}{9}-\frac{5}{6}\times \frac{20}{9}$$

Multiply \frac{5}{6} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50}{9}-\frac{5\times 20}{6\times 9}$$

Do the multiplications in the fraction \frac{5\times 20}{6\times 9}.

$$\frac{50}{9}-\frac{100}{54}$$

Reduce the fraction \frac{100}{54} to lowest terms by extracting and canceling out 2.

$$\frac{50}{9}-\frac{50}{27}$$

Least common multiple of 9 and 27 is 27. Convert \frac{50}{9} and \frac{50}{27} to fractions with denominator 27.

$$\frac{150}{27}-\frac{50}{27}$$

Since \frac{150}{27} and \frac{50}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{150-50}{27}$$

Subtract 50 from 150 to get 100.

$$\frac{100}{27}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2}}{3 ^ {3}} = 3\frac{19}{27} = 3.7037037037037037$$