Solve ((5)/(2)+(12)/(7))\div((8)/(5)\times(20)/(12))

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Question

$$( \frac{ 5 }{ 2 } + \frac{ 12 }{ 7 } ) \div ( \frac{ 8 }{ 5 } \times \frac{ 20 }{ 12 } )$$

Evaluate

$\frac{177}{112}\approx 1.580357143$

Solution Steps

Least common multiple of $2$ and $7$ is $14$. Convert $\frac{5}{2}$ and $\frac{12}{7}$ to fractions with denominator $14$.

$$\frac{\frac{35}{14}+\frac{24}{14}}{\frac{8}{5}\times \frac{20}{12}}$$

Since $\frac{35}{14}$ and $\frac{24}{14}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{35+24}{14}}{\frac{8}{5}\times \frac{20}{12}}$$

Add $35$ and $24$ to get $59$.

$$\frac{\frac{59}{14}}{\frac{8}{5}\times \frac{20}{12}}$$

Reduce the fraction $\frac{20}{12}$ to lowest terms by extracting and canceling out $4$.

$$\frac{\frac{59}{14}}{\frac{8}{5}\times \frac{5}{3}}$$

Multiply $\frac{8}{5}$ times $\frac{5}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{59}{14}}{\frac{8\times 5}{5\times 3}}$$

Cancel out $5$ in both numerator and denominator.

$$\frac{\frac{59}{14}}{\frac{8}{3}}$$

Divide $\frac{59}{14}$ by $\frac{8}{3}$ by multiplying $\frac{59}{14}$ by the reciprocal of $\frac{8}{3}$.

$$\frac{59}{14}\times \frac{3}{8}$$

Multiply $\frac{59}{14}$ times $\frac{3}{8}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{59\times 3}{14\times 8}$$

Do the multiplications in the fraction $\frac{59\times 3}{14\times 8}$.

$$\frac{177}{112}$$

Show Solution

Factor

$\frac{3 \cdot 59}{2 ^ {4} \cdot 7} = 1\frac{65}{112} = 1.5803571428571428$