Solve ((5)/(9)-1(1)/(6)\times(1)/(2))\div(5)/(9)+(1)/(3)

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Question

$$( \frac{ 5 }{ 9 } -1 \frac{ 1 }{ 6 } \times \frac{ 1 }{ 2 } ) \div \frac{ 5 }{ 9 } + \frac{ 1 }{ 3 }$$

Evaluate

$\frac{17}{60}\approx 0.283333333$

Solution Steps

Multiply $1$ and $6$ to get $6$.

$$\frac{\frac{5}{9}-\frac{6+1}{6}\times \frac{1}{2}}{\frac{5}{9}}+\frac{1}{3}$$

Add $6$ and $1$ to get $7$.

$$\frac{\frac{5}{9}-\frac{7}{6}\times \frac{1}{2}}{\frac{5}{9}}+\frac{1}{3}$$

Multiply $\frac{7}{6}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{9}-\frac{7\times 1}{6\times 2}}{\frac{5}{9}}+\frac{1}{3}$$

Do the multiplications in the fraction $\frac{7\times 1}{6\times 2}$.

$$\frac{\frac{5}{9}-\frac{7}{12}}{\frac{5}{9}}+\frac{1}{3}$$

Least common multiple of $9$ and $12$ is $36$. Convert $\frac{5}{9}$ and $\frac{7}{12}$ to fractions with denominator $36$.

$$\frac{\frac{20}{36}-\frac{21}{36}}{\frac{5}{9}}+\frac{1}{3}$$

Since $\frac{20}{36}$ and $\frac{21}{36}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20-21}{36}}{\frac{5}{9}}+\frac{1}{3}$$

Subtract $21$ from $20$ to get $-1$.

$$\frac{-\frac{1}{36}}{\frac{5}{9}}+\frac{1}{3}$$

Divide $-\frac{1}{36}$ by $\frac{5}{9}$ by multiplying $-\frac{1}{36}$ by the reciprocal of $\frac{5}{9}$.

$$-\frac{1}{36}\times \frac{9}{5}+\frac{1}{3}$$

Multiply $-\frac{1}{36}$ times $\frac{9}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9}{36\times 5}+\frac{1}{3}$$

Do the multiplications in the fraction $\frac{-9}{36\times 5}$.

$$\frac{-9}{180}+\frac{1}{3}$$

Reduce the fraction $\frac{-9}{180}$ to lowest terms by extracting and canceling out $9$.

$$-\frac{1}{20}+\frac{1}{3}$$

Least common multiple of $20$ and $3$ is $60$. Convert $-\frac{1}{20}$ and $\frac{1}{3}$ to fractions with denominator $60$.

$$-\frac{3}{60}+\frac{20}{60}$$

Since $-\frac{3}{60}$ and $\frac{20}{60}$ have the same denominator, add them by adding their numerators.

$$\frac{-3+20}{60}$$

Add $-3$ and $20$ to get $17$.

$$\frac{17}{60}$$

Show Solution

Factor

$\frac{17}{2 ^ {2} \cdot 3 \cdot 5} = 0.2833333333333333$