Solve 4 4 5 *(1+ 2 5 *2 3 4 ) binom 3 8 *4-3* 3 8 )* 4 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

$$\frac{4\frac{4}{5}\cdot(1+\frac{2}{5}\cdot2\frac{3}{4})}{\binom{3}{8}\cdot4-3\cdot\frac{3}{8})\cdot\frac{4}{3}}=$$

Evaluate

$\frac{32}{7}\approx 4.571428571$

Solution Steps

Multiply $4$ and $5$ to get $20$.

$$\frac{\frac{\frac{20+4}{5}}{1+\frac{2}{5}\times \frac{2\times 4+3}{4}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Add $20$ and $4$ to get $24$.

$$\frac{\frac{\frac{24}{5}}{1+\frac{2}{5}\times \frac{2\times 4+3}{4}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Multiply $2$ and $4$ to get $8$.

$$\frac{\frac{\frac{24}{5}}{1+\frac{2}{5}\times \frac{8+3}{4}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Add $8$ and $3$ to get $11$.

$$\frac{\frac{\frac{24}{5}}{1+\frac{2}{5}\times \frac{11}{4}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Multiply $\frac{2}{5}$ times $\frac{11}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{24}{5}}{1+\frac{2\times 11}{5\times 4}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Do the multiplications in the fraction $\frac{2\times 11}{5\times 4}$.

$$\frac{\frac{\frac{24}{5}}{1+\frac{22}{20}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Reduce the fraction $\frac{22}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{\frac{24}{5}}{1+\frac{11}{10}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Convert $1$ to fraction $\frac{10}{10}$.

$$\frac{\frac{\frac{24}{5}}{\frac{10}{10}+\frac{11}{10}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Since $\frac{10}{10}$ and $\frac{11}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{24}{5}}{\frac{10+11}{10}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Add $10$ and $11$ to get $21$.

$$\frac{\frac{\frac{24}{5}}{\frac{21}{10}}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Divide $\frac{24}{5}$ by $\frac{21}{10}$ by multiplying $\frac{24}{5}$ by the reciprocal of $\frac{21}{10}$.

$$\frac{\frac{24}{5}\times \frac{10}{21}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Multiply $\frac{24}{5}$ times $\frac{10}{21}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{24\times 10}{5\times 21}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Do the multiplications in the fraction $\frac{24\times 10}{5\times 21}$.

$$\frac{\frac{240}{105}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Reduce the fraction $\frac{240}{105}$ to lowest terms by extracting and canceling out $15$.

$$\frac{\frac{16}{7}}{\left(\frac{3}{8}\times 4-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Express $\frac{3}{8}\times 4$ as a single fraction.

$$\frac{\frac{16}{7}}{\left(\frac{3\times 4}{8}-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Multiply $3$ and $4$ to get $12$.

$$\frac{\frac{16}{7}}{\left(\frac{12}{8}-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Reduce the fraction $\frac{12}{8}$ to lowest terms by extracting and canceling out $4$.

$$\frac{\frac{16}{7}}{\left(\frac{3}{2}-3\times \frac{3}{8}\right)\times \frac{4}{3}}$$

Express $3\times \frac{3}{8}$ as a single fraction.

$$\frac{\frac{16}{7}}{\left(\frac{3}{2}-\frac{3\times 3}{8}\right)\times \frac{4}{3}}$$

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

$$\frac{\frac{16}{7}}{\left(\frac{3}{2}-\frac{9}{8}\right)\times \frac{4}{3}}$$

Least common multiple of $2$ and $8$ is $8$. Convert $\frac{3}{2}$ and $\frac{9}{8}$ to fractions with denominator $8$.

$$\frac{\frac{16}{7}}{\left(\frac{12}{8}-\frac{9}{8}\right)\times \frac{4}{3}}$$

Since $\frac{12}{8}$ and $\frac{9}{8}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16}{7}}{\frac{12-9}{8}\times \frac{4}{3}}$$

Subtract $9$ from $12$ to get $3$.

$$\frac{\frac{16}{7}}{\frac{3}{8}\times \frac{4}{3}}$$

Multiply $\frac{3}{8}$ times $\frac{4}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{16}{7}}{\frac{3\times 4}{8\times 3}}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{\frac{16}{7}}{\frac{4}{8}}$$

Reduce the fraction $\frac{4}{8}$ to lowest terms by extracting and canceling out $4$.

$$\frac{\frac{16}{7}}{\frac{1}{2}}$$

Divide $\frac{16}{7}$ by $\frac{1}{2}$ by multiplying $\frac{16}{7}$ by the reciprocal of $\frac{1}{2}$.

$$\frac{16}{7}\times 2$$

Express $\frac{16}{7}\times 2$ as a single fraction.

$$\frac{16\times 2}{7}$$

Multiply $16$ and $2$ to get $32$.

$$\frac{32}{7}$$

Factor

$\frac{2 ^ {5}}{7} = 4\frac{4}{7} = 4.571428571428571$