Solve (2\times(3)/(4)-(5)/(6)\times1\times(1)/(3))\div((5\times(1)/(35)-x)\times12\times(1)/(4)

Question

$$(2 \times \frac{ 3 }{ 4 } - \frac{ 5 }{ 6 } \times 1 \times \frac{ 1 }{ 3 } ) \div ((5 \times \frac{ 1 }{ 35 } -x) \times 12 \times \frac{ 1 }{ 4 }$$

Evaluate

$\frac{77}{27\left(1-7x\right)}$

Solution Steps

Express $2\times \frac{3}{4}$ as a single fraction.

$$\frac{\frac{2\times 3}{4}-\frac{5}{6}\times 1\times \frac{1}{3}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Multiply $2$ and $3$ to get $6$.

$$\frac{\frac{6}{4}-\frac{5}{6}\times 1\times \frac{1}{3}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Reduce the fraction $\frac{6}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{3}{2}-\frac{5}{6}\times 1\times \frac{1}{3}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Multiply $\frac{5}{6}$ and $1$ to get $\frac{5}{6}$.

$$\frac{\frac{3}{2}-\frac{5}{6}\times \frac{1}{3}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Multiply $\frac{5}{6}$ times $\frac{1}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{2}-\frac{5\times 1}{6\times 3}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Do the multiplications in the fraction $\frac{5\times 1}{6\times 3}$.

$$\frac{\frac{3}{2}-\frac{5}{18}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Least common multiple of $2$ and $18$ is $18$. Convert $\frac{3}{2}$ and $\frac{5}{18}$ to fractions with denominator $18$.

$$\frac{\frac{27}{18}-\frac{5}{18}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Since $\frac{27}{18}$ and $\frac{5}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-5}{18}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Subtract $5$ from $27$ to get $22$.

$$\frac{\frac{22}{18}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Reduce the fraction $\frac{22}{18}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{11}{9}}{\left(5\times \frac{1}{35}-x\right)\times 12\times \frac{1}{4}}$$

Multiply $5$ and $\frac{1}{35}$ to get $\frac{5}{35}$.

$$\frac{\frac{11}{9}}{\left(\frac{5}{35}-x\right)\times 12\times \frac{1}{4}}$$

Reduce the fraction $\frac{5}{35}$ to lowest terms by extracting and canceling out $5$.

$$\frac{\frac{11}{9}}{\left(\frac{1}{7}-x\right)\times 12\times \frac{1}{4}}$$

Multiply $12$ and $\frac{1}{4}$ to get $\frac{12}{4}$.

$$\frac{\frac{11}{9}}{\left(\frac{1}{7}-x\right)\times \frac{12}{4}}$$

Divide $12$ by $4$ to get $3$.

$$\frac{\frac{11}{9}}{\left(\frac{1}{7}-x\right)\times 3}$$

Express $\frac{\frac{11}{9}}{\left(\frac{1}{7}-x\right)\times 3}$ as a single fraction.

$$\frac{11}{9\left(\frac{1}{7}-x\right)\times 3}$$

Multiply $9$ and $3$ to get $27$.

$$\frac{11}{27\left(\frac{1}{7}-x\right)}$$

Use the distributive property to multiply $27$ by $\frac{1}{7}-x$.

$$\frac{11}{27\times \frac{1}{7}-27x}$$

Multiply $27$ and $\frac{1}{7}$ to get $\frac{27}{7}$.

$$\frac{11}{\frac{27}{7}-27x}$$

Show Solution

Expand

$\frac{11}{27\left(\frac{1}{7}-x\right)}$