Solve (3)/(10)\times(8)/(9)\div(20)/(27)+(4)/(9)

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Question

$$\frac{ 3 }{ 10 } \times \frac{ 8 }{ 9 } \div \frac{ 20 }{ 27 } + \frac{ 4 }{ 9 }$$

Evaluate

$\frac{181}{225}\approx 0.804444444$

Solution Steps

Multiply $\frac{3}{10}$ times $\frac{8}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 8}{10\times 9}}{\frac{20}{27}}+\frac{4}{9}$$

Do the multiplications in the fraction $\frac{3\times 8}{10\times 9}$.

$$\frac{\frac{24}{90}}{\frac{20}{27}}+\frac{4}{9}$$

Reduce the fraction $\frac{24}{90}$ to lowest terms by extracting and canceling out $6$.

$$\frac{\frac{4}{15}}{\frac{20}{27}}+\frac{4}{9}$$

Divide $\frac{4}{15}$ by $\frac{20}{27}$ by multiplying $\frac{4}{15}$ by the reciprocal of $\frac{20}{27}$.

$$\frac{4}{15}\times \frac{27}{20}+\frac{4}{9}$$

Multiply $\frac{4}{15}$ times $\frac{27}{20}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 27}{15\times 20}+\frac{4}{9}$$

Do the multiplications in the fraction $\frac{4\times 27}{15\times 20}$.

$$\frac{108}{300}+\frac{4}{9}$$

Reduce the fraction $\frac{108}{300}$ to lowest terms by extracting and canceling out $12$.

$$\frac{9}{25}+\frac{4}{9}$$

Least common multiple of $25$ and $9$ is $225$. Convert $\frac{9}{25}$ and $\frac{4}{9}$ to fractions with denominator $225$.

$$\frac{81}{225}+\frac{100}{225}$$

Since $\frac{81}{225}$ and $\frac{100}{225}$ have the same denominator, add them by adding their numerators.

$$\frac{81+100}{225}$$

Add $81$ and $100$ to get $181$.

$$\frac{181}{225}$$

Show Solution

Factor

$\frac{181}{3 ^ {2} \cdot 5 ^ {2}} = 0.8044444444444444$