Solve (iii) (1/6 + 7/12 * or * 3/7)/(2/3 * 3/4 - 2/3 + 5/3) | 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

$$\frac { \frac { 1 } { 6 } + \frac { 7 } { 12 } \frac { 3 } { 7 } } { \frac { 2 } { 3 } \times \frac { 3 } { 4 } - \frac { 2 } { 3 } \div \frac { 5 } { 3 } }$$

Evaluate

$\frac{25}{6}\approx 4.166666667$

Solution Steps

Multiply $\frac{7}{12}$ times $\frac{3}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{6}+\frac{7\times 3}{12\times 7}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Cancel out $7$ in both numerator and denominator.

$$\frac{\frac{1}{6}+\frac{3}{12}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Reduce the fraction $\frac{3}{12}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{1}{6}+\frac{1}{4}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Least common multiple of $6$ and $4$ is $12$. Convert $\frac{1}{6}$ and $\frac{1}{4}$ to fractions with denominator $12$.

$$\frac{\frac{2}{12}+\frac{3}{12}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Since $\frac{2}{12}$ and $\frac{3}{12}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{2+3}{12}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Add $2$ and $3$ to get $5$.

$$\frac{\frac{5}{12}}{\frac{2}{3}\times \frac{3}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Multiply $\frac{2}{3}$ times $\frac{3}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{12}}{\frac{2\times 3}{3\times 4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{\frac{5}{12}}{\frac{2}{4}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{5}{12}}{\frac{1}{2}-\frac{\frac{2}{3}}{\frac{5}{3}}}$$

Divide $\frac{2}{3}$ by $\frac{5}{3}$ by multiplying $\frac{2}{3}$ by the reciprocal of $\frac{5}{3}$.

$$\frac{\frac{5}{12}}{\frac{1}{2}-\frac{2}{3}\times \frac{3}{5}}$$

Multiply $\frac{2}{3}$ times $\frac{3}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{12}}{\frac{1}{2}-\frac{2\times 3}{3\times 5}}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{\frac{5}{12}}{\frac{1}{2}-\frac{2}{5}}$$

Least common multiple of $2$ and $5$ is $10$. Convert $\frac{1}{2}$ and $\frac{2}{5}$ to fractions with denominator $10$.

$$\frac{\frac{5}{12}}{\frac{5}{10}-\frac{4}{10}}$$

Since $\frac{5}{10}$ and $\frac{4}{10}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{12}}{\frac{5-4}{10}}$$

Subtract $4$ from $5$ to get $1$.

$$\frac{\frac{5}{12}}{\frac{1}{10}}$$

Divide $\frac{5}{12}$ by $\frac{1}{10}$ by multiplying $\frac{5}{12}$ by the reciprocal of $\frac{1}{10}$.

$$\frac{5}{12}\times 10$$

Express $\frac{5}{12}\times 10$ as a single fraction.

$$\frac{5\times 10}{12}$$

Multiply $5$ and $10$ to get $50$.

$$\frac{50}{12}$$

Reduce the fraction $\frac{50}{12}$ to lowest terms by extracting and canceling out $2$.

$$\frac{25}{6}$$

Factor

$\frac{5 ^ {2}}{2 \cdot 3} = 4\frac{1}{6} = 4.166666666666667$