Solve (5/3 + 5/6)/(17/6 - 10/3) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{\frac{5}{3}+\frac{5}{6}}{\frac{17}{6}-\frac{10}{3}}$$

Evaluate

$-5$

Solution Steps

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{5}{3}$ and $\frac{5}{6}$ to fractions with denominator $6$.

$$\frac{\frac{10}{6}+\frac{5}{6}}{\frac{17}{6}-\frac{10}{3}}$$

Since $\frac{10}{6}$ and $\frac{5}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+5}{6}}{\frac{17}{6}-\frac{10}{3}}$$

Add $10$ and $5$ to get $15$.

$$\frac{\frac{15}{6}}{\frac{17}{6}-\frac{10}{3}}$$

Reduce the fraction $\frac{15}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{5}{2}}{\frac{17}{6}-\frac{10}{3}}$$

Least common multiple of $6$ and $3$ is $6$. Convert $\frac{17}{6}$ and $\frac{10}{3}$ to fractions with denominator $6$.

$$\frac{\frac{5}{2}}{\frac{17}{6}-\frac{20}{6}}$$

Since $\frac{17}{6}$ and $\frac{20}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}}{\frac{17-20}{6}}$$

Subtract $20$ from $17$ to get $-3$.

$$\frac{\frac{5}{2}}{\frac{-3}{6}}$$

Reduce the fraction $\frac{-3}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{5}{2}}{-\frac{1}{2}}$$

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

$$\frac{5}{2}\left(-2\right)$$

Express $\frac{5}{2}\left(-2\right)$ as a single fraction.

$$\frac{5\left(-2\right)}{2}$$

Multiply $5$ and $-2$ to get $-10$.

$$\frac{-10}{2}$$

Divide $-10$ by $2$ to get $-5$.

$$-5$$

Factor

$-5$