Solve ((8)/(7)\times(2)/(5)+(3)/(5))\div(1)/(2)+(3)/(5)=

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Question

$$( \frac{ 8 }{ 7 } \times \frac{ 2 }{ 5 } + \frac{ 3 }{ 5 } ) \div \frac{ 1 }{ 2 } + \frac{ 3 }{ 5 } =$$

Evaluate

$\frac{19}{7}\approx 2.714285714$

Solution Steps

Multiply $\frac{8}{7}$ times $\frac{2}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8\times 2}{7\times 5}+\frac{3}{5}}{\frac{1}{2}}+\frac{3}{5}$$

Do the multiplications in the fraction $\frac{8\times 2}{7\times 5}$.

$$\frac{\frac{16}{35}+\frac{3}{5}}{\frac{1}{2}}+\frac{3}{5}$$

Least common multiple of $35$ and $5$ is $35$. Convert $\frac{16}{35}$ and $\frac{3}{5}$ to fractions with denominator $35$.

$$\frac{\frac{16}{35}+\frac{21}{35}}{\frac{1}{2}}+\frac{3}{5}$$

Since $\frac{16}{35}$ and $\frac{21}{35}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+21}{35}}{\frac{1}{2}}+\frac{3}{5}$$

Add $16$ and $21$ to get $37$.

$$\frac{\frac{37}{35}}{\frac{1}{2}}+\frac{3}{5}$$

Divide $\frac{37}{35}$ by $\frac{1}{2}$ by multiplying $\frac{37}{35}$ by the reciprocal of $\frac{1}{2}$.

$$\frac{37}{35}\times 2+\frac{3}{5}$$

Express $\frac{37}{35}\times 2$ as a single fraction.

$$\frac{37\times 2}{35}+\frac{3}{5}$$

Multiply $37$ and $2$ to get $74$.

$$\frac{74}{35}+\frac{3}{5}$$

Least common multiple of $35$ and $5$ is $35$. Convert $\frac{74}{35}$ and $\frac{3}{5}$ to fractions with denominator $35$.

$$\frac{74}{35}+\frac{21}{35}$$

Since $\frac{74}{35}$ and $\frac{21}{35}$ have the same denominator, add them by adding their numerators.

$$\frac{74+21}{35}$$

Add $74$ and $21$ to get $95$.

$$\frac{95}{35}$$

Reduce the fraction $\frac{95}{35}$ to lowest terms by extracting and canceling out $5$.

$$\frac{19}{7}$$

Show Solution

Factor

$\frac{19}{7} = 2\frac{5}{7} = 2.7142857142857144$