Solve (3)/(2)\div((10)/(3)+(21)/(5)-(13)/(2))

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Question

$$\frac{ 3 }{ 2 } \div ( \frac{ 10 }{ 3 } + \frac{ 21 }{ 5 } - \frac{ 13 }{ 2 } )$$

Evaluate

$\frac{45}{31}\approx 1.451612903$

Solution Steps

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{10}{3}$ and $\frac{21}{5}$ to fractions with denominator $15$.

$$\frac{\frac{3}{2}}{\frac{50}{15}+\frac{63}{15}-\frac{13}{2}}$$

Since $\frac{50}{15}$ and $\frac{63}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}}{\frac{50+63}{15}-\frac{13}{2}}$$

Add $50$ and $63$ to get $113$.

$$\frac{\frac{3}{2}}{\frac{113}{15}-\frac{13}{2}}$$

Least common multiple of $15$ and $2$ is $30$. Convert $\frac{113}{15}$ and $\frac{13}{2}$ to fractions with denominator $30$.

$$\frac{\frac{3}{2}}{\frac{226}{30}-\frac{195}{30}}$$

Since $\frac{226}{30}$ and $\frac{195}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}}{\frac{226-195}{30}}$$

Subtract $195$ from $226$ to get $31$.

$$\frac{\frac{3}{2}}{\frac{31}{30}}$$

Divide $\frac{3}{2}$ by $\frac{31}{30}$ by multiplying $\frac{3}{2}$ by the reciprocal of $\frac{31}{30}$.

$$\frac{3}{2}\times \frac{30}{31}$$

Multiply $\frac{3}{2}$ times $\frac{30}{31}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 30}{2\times 31}$$

Do the multiplications in the fraction $\frac{3\times 30}{2\times 31}$.

$$\frac{90}{62}$$

Reduce the fraction $\frac{90}{62}$ to lowest terms by extracting and canceling out $2$.

$$\frac{45}{31}$$

Show Solution

Factor

$\frac{3 ^ {2} \cdot 5}{31} = 1\frac{14}{31} = 1.4516129032258065$