Solve (1)/(2)\times((4)/(5))-(5)/(36)\times(6)/(25)+(4)/(72)\div(1)/(6)-(5)/(18)

Question

$$\frac{ 1 }{ 2 } \times ( \frac{ 4 }{ 5 } )- \frac{ 5 }{ 36 } \times \frac{ 6 }{ 25 } + \frac{ 4 }{ 72 } \div \frac{ 1 }{ 6 } - \frac{ 5 }{ 18 }$$

Evaluate

$\frac{19}{45}\approx 0.422222222$

Solution Steps

Multiply $\frac{1}{2}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 4}{2\times 5}-\frac{5}{36}\times \frac{6}{25}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Do the multiplications in the fraction $\frac{1\times 4}{2\times 5}$.

$$\frac{4}{10}-\frac{5}{36}\times \frac{6}{25}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Reduce the fraction $\frac{4}{10}$ to lowest terms by extracting and canceling out $2$.

$$\frac{2}{5}-\frac{5}{36}\times \frac{6}{25}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Multiply $\frac{5}{36}$ times $\frac{6}{25}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{5\times 6}{36\times 25}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Do the multiplications in the fraction $\frac{5\times 6}{36\times 25}$.

$$\frac{2}{5}-\frac{30}{900}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Reduce the fraction $\frac{30}{900}$ to lowest terms by extracting and canceling out $30$.

$$\frac{2}{5}-\frac{1}{30}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Least common multiple of $5$ and $30$ is $30$. Convert $\frac{2}{5}$ and $\frac{1}{30}$ to fractions with denominator $30$.

$$\frac{12}{30}-\frac{1}{30}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Since $\frac{12}{30}$ and $\frac{1}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-1}{30}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Subtract $1$ from $12$ to get $11$.

$$\frac{11}{30}+\frac{\frac{4}{72}}{\frac{1}{6}}-\frac{5}{18}$$

Divide $\frac{4}{72}$ by $\frac{1}{6}$ by multiplying $\frac{4}{72}$ by the reciprocal of $\frac{1}{6}$.

$$\frac{11}{30}+\frac{4\times 6}{72}-\frac{5}{18}$$

Multiply $4$ and $6$ to get $24$.

$$\frac{11}{30}+\frac{24}{72}-\frac{5}{18}$$

Reduce the fraction $\frac{24}{72}$ to lowest terms by extracting and canceling out $24$.

$$\frac{11}{30}+\frac{1}{3}-\frac{5}{18}$$

Least common multiple of $30$ and $3$ is $30$. Convert $\frac{11}{30}$ and $\frac{1}{3}$ to fractions with denominator $30$.

$$\frac{11}{30}+\frac{10}{30}-\frac{5}{18}$$

Since $\frac{11}{30}$ and $\frac{10}{30}$ have the same denominator, add them by adding their numerators.

$$\frac{11+10}{30}-\frac{5}{18}$$

Add $11$ and $10$ to get $21$.

$$\frac{21}{30}-\frac{5}{18}$$

Reduce the fraction $\frac{21}{30}$ to lowest terms by extracting and canceling out $3$.

$$\frac{7}{10}-\frac{5}{18}$$

Least common multiple of $10$ and $18$ is $90$. Convert $\frac{7}{10}$ and $\frac{5}{18}$ to fractions with denominator $90$.

$$\frac{63}{90}-\frac{25}{90}$$

Since $\frac{63}{90}$ and $\frac{25}{90}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-25}{90}$$

Subtract $25$ from $63$ to get $38$.

$$\frac{38}{90}$$

Reduce the fraction $\frac{38}{90}$ to lowest terms by extracting and canceling out $2$.

$$\frac{19}{45}$$

Show Solution

Factor

$\frac{19}{3 ^ {2} \cdot 5} = 0.4222222222222222$

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