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

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Question

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

Evaluate

$\frac{179}{80}=2.2375$

Solution Steps

Reduce the fraction $\frac{2}{8}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{7}{8}\times \frac{1}{4}+\frac{3}{5}}{\frac{1}{2}}+\frac{3}{5}$$

Multiply $\frac{7}{8}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 1}{8\times 4}+\frac{3}{5}}{\frac{1}{2}}+\frac{3}{5}$$

Do the multiplications in the fraction $\frac{7\times 1}{8\times 4}$.

$$\frac{\frac{7}{32}+\frac{3}{5}}{\frac{1}{2}}+\frac{3}{5}$$

Least common multiple of $32$ and $5$ is $160$. Convert $\frac{7}{32}$ and $\frac{3}{5}$ to fractions with denominator $160$.

$$\frac{\frac{35}{160}+\frac{96}{160}}{\frac{1}{2}}+\frac{3}{5}$$

Since $\frac{35}{160}$ and $\frac{96}{160}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{35+96}{160}}{\frac{1}{2}}+\frac{3}{5}$$

Add $35$ and $96$ to get $131$.

$$\frac{\frac{131}{160}}{\frac{1}{2}}+\frac{3}{5}$$

Divide $\frac{131}{160}$ by $\frac{1}{2}$ by multiplying $\frac{131}{160}$ by the reciprocal of $\frac{1}{2}$.

$$\frac{131}{160}\times 2+\frac{3}{5}$$

Express $\frac{131}{160}\times 2$ as a single fraction.

$$\frac{131\times 2}{160}+\frac{3}{5}$$

Multiply $131$ and $2$ to get $262$.

$$\frac{262}{160}+\frac{3}{5}$$

Reduce the fraction $\frac{262}{160}$ to lowest terms by extracting and canceling out $2$.

$$\frac{131}{80}+\frac{3}{5}$$

Least common multiple of $80$ and $5$ is $80$. Convert $\frac{131}{80}$ and $\frac{3}{5}$ to fractions with denominator $80$.

$$\frac{131}{80}+\frac{48}{80}$$

Since $\frac{131}{80}$ and $\frac{48}{80}$ have the same denominator, add them by adding their numerators.

$$\frac{131+48}{80}$$

Add $131$ and $48$ to get $179$.

$$\frac{179}{80}$$

Show Solution

Factor

$\frac{179}{2 ^ {4} \cdot 5} = 2\frac{19}{80} = 2.2375$