Solve (3)/(5)\div(1)/(2)+(2)/(3)\times(8)/(9)-(3)/(4)=

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Question

$$\frac{ 3 }{ 5 } \div \frac{ 1 }{ 2 } + \frac{ 2 }{ 3 } \times \frac{ 8 }{ 9 } - \frac{ 3 }{ 4 } =$$

Evaluate

$\frac{563}{540}\approx 1.042592593$

Solution Steps

Divide $\frac{3}{5}$ by $\frac{1}{2}$ by multiplying $\frac{3}{5}$ by the reciprocal of $\frac{1}{2}$.

$$\frac{3}{5}\times 2+\frac{2}{3}\times \frac{8}{9}-\frac{3}{4}$$

Express $\frac{3}{5}\times 2$ as a single fraction.

$$\frac{3\times 2}{5}+\frac{2}{3}\times \frac{8}{9}-\frac{3}{4}$$

Multiply $3$ and $2$ to get $6$.

$$\frac{6}{5}+\frac{2}{3}\times \frac{8}{9}-\frac{3}{4}$$

Multiply $\frac{2}{3}$ times $\frac{8}{9}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{5}+\frac{2\times 8}{3\times 9}-\frac{3}{4}$$

Do the multiplications in the fraction $\frac{2\times 8}{3\times 9}$.

$$\frac{6}{5}+\frac{16}{27}-\frac{3}{4}$$

Least common multiple of $5$ and $27$ is $135$. Convert $\frac{6}{5}$ and $\frac{16}{27}$ to fractions with denominator $135$.

$$\frac{162}{135}+\frac{80}{135}-\frac{3}{4}$$

Since $\frac{162}{135}$ and $\frac{80}{135}$ have the same denominator, add them by adding their numerators.

$$\frac{162+80}{135}-\frac{3}{4}$$

Add $162$ and $80$ to get $242$.

$$\frac{242}{135}-\frac{3}{4}$$

Least common multiple of $135$ and $4$ is $540$. Convert $\frac{242}{135}$ and $\frac{3}{4}$ to fractions with denominator $540$.

$$\frac{968}{540}-\frac{405}{540}$$

Since $\frac{968}{540}$ and $\frac{405}{540}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{968-405}{540}$$

Subtract $405$ from $968$ to get $563$.

$$\frac{563}{540}$$

Show Solution

Factor

$\frac{563}{2 ^ {2} \cdot 3 ^ {3} \cdot 5} = 1\frac{23}{540} = 1.0425925925925925$