Solve ((1)/(4)+(1)/(4)-(3)/(8))\times((36)/(45)\div(18)/(5))

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Question

$$( \frac{ 1 }{ 4 } + \frac{ 1 }{ 4 } - \frac{ 3 }{ 8 } ) \times ( \frac{ 36 }{ 45 } \div \frac{ 18 }{ 5 } )$$

Evaluate

$\frac{1}{36}\approx 0.027777778$

Solution Steps

Since $\frac{1}{4}$ and $\frac{1}{4}$ have the same denominator, add them by adding their numerators.

$$\left(\frac{1+1}{4}-\frac{3}{8}\right)\times \frac{\frac{36}{45}}{\frac{18}{5}}$$

Add $1$ and $1$ to get $2$.

$$\left(\frac{2}{4}-\frac{3}{8}\right)\times \frac{\frac{36}{45}}{\frac{18}{5}}$$

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

$$\left(\frac{1}{2}-\frac{3}{8}\right)\times \frac{\frac{36}{45}}{\frac{18}{5}}$$

Least common multiple of $2$ and $8$ is $8$. Convert $\frac{1}{2}$ and $\frac{3}{8}$ to fractions with denominator $8$.

$$\left(\frac{4}{8}-\frac{3}{8}\right)\times \frac{\frac{36}{45}}{\frac{18}{5}}$$

Since $\frac{4}{8}$ and $\frac{3}{8}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{8}\times \frac{\frac{36}{45}}{\frac{18}{5}}$$

Subtract $3$ from $4$ to get $1$.

$$\frac{1}{8}\times \frac{\frac{36}{45}}{\frac{18}{5}}$$

Divide $\frac{36}{45}$ by $\frac{18}{5}$ by multiplying $\frac{36}{45}$ by the reciprocal of $\frac{18}{5}$.

$$\frac{1}{8}\times \frac{36\times 5}{45\times 18}$$

Cancel out $2\times 5\times 9$ in both numerator and denominator.

$$\frac{1}{8}\times \frac{2}{9}$$

Multiply $\frac{1}{8}$ times $\frac{2}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{8\times 9}$$

Do the multiplications in the fraction $\frac{1\times 2}{8\times 9}$.

$$\frac{2}{72}$$

Reduce the fraction $\frac{2}{72}$ to lowest terms by extracting and canceling out $2$.

$$\frac{1}{36}$$

Show Solution

Factor

$\frac{1}{2 ^ {2} \cdot 3 ^ {2}} = 0.027777777777777776$