Solve 1 1/3 * 4[1 2/3 - 4\{5/2 * (2/2 - 1/2 + 2/4)\}]

Question

$$1\frac{1}{3}\times4[1\frac{2}{3}-4\{\frac{5}{2}\times(\frac{2}{2}-\frac{1}{2}+\frac{2}{4})\}]$$

Evaluate

$-\frac{400}{9}\approx -44.444444444$

Solution Steps

Divide $2$ by $2$ to get $1$.

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

Multiply $1$ and $3$ to get $3$.

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

Add $3$ and $1$ to get $4$.

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

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

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

Multiply $4$ and $4$ to get $16$.

$$\frac{16}{3}\left(\frac{1\times 3+2}{3}-4\times \frac{5}{2}\left(1-\frac{1}{2}+\frac{2}{4}\right)\right)$$

Multiply $1$ and $3$ to get $3$.

$$\frac{16}{3}\left(\frac{3+2}{3}-4\times \frac{5}{2}\left(1-\frac{1}{2}+\frac{2}{4}\right)\right)$$

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

$$\frac{16}{3}\left(\frac{5}{3}-4\times \frac{5}{2}\left(1-\frac{1}{2}+\frac{2}{4}\right)\right)$$

Express $4\times \frac{5}{2}$ as a single fraction.

$$\frac{16}{3}\left(\frac{5}{3}-\frac{4\times 5}{2}\left(1-\frac{1}{2}+\frac{2}{4}\right)\right)$$

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

$$\frac{16}{3}\left(\frac{5}{3}-\frac{20}{2}\left(1-\frac{1}{2}+\frac{2}{4}\right)\right)$$

Divide $20$ by $2$ to get $10$.

$$\frac{16}{3}\left(\frac{5}{3}-10\left(1-\frac{1}{2}+\frac{2}{4}\right)\right)$$

Convert $1$ to fraction $\frac{2}{2}$.

$$\frac{16}{3}\left(\frac{5}{3}-10\left(\frac{2}{2}-\frac{1}{2}+\frac{2}{4}\right)\right)$$

Since $\frac{2}{2}$ and $\frac{1}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{3}\left(\frac{5}{3}-10\left(\frac{2-1}{2}+\frac{2}{4}\right)\right)$$

Subtract $1$ from $2$ to get $1$.

$$\frac{16}{3}\left(\frac{5}{3}-10\left(\frac{1}{2}+\frac{2}{4}\right)\right)$$

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

$$\frac{16}{3}\left(\frac{5}{3}-10\left(\frac{1}{2}+\frac{1}{2}\right)\right)$$

Since $\frac{1}{2}$ and $\frac{1}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{16}{3}\left(\frac{5}{3}-10\times \frac{1+1}{2}\right)$$

Add $1$ and $1$ to get $2$.

$$\frac{16}{3}\left(\frac{5}{3}-10\times \frac{2}{2}\right)$$

Divide $2$ by $2$ to get $1$.

$$\frac{16}{3}\left(\frac{5}{3}-10\times 1\right)$$

Multiply $10$ and $1$ to get $10$.

$$\frac{16}{3}\left(\frac{5}{3}-10\right)$$

Convert $10$ to fraction $\frac{30}{3}$.

$$\frac{16}{3}\left(\frac{5}{3}-\frac{30}{3}\right)$$

Since $\frac{5}{3}$ and $\frac{30}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{16}{3}\times \frac{5-30}{3}$$

Subtract $30$ from $5$ to get $-25$.

$$\frac{16}{3}\left(-\frac{25}{3}\right)$$

Multiply $\frac{16}{3}$ times $-\frac{25}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\left(-25\right)}{3\times 3}$$

Do the multiplications in the fraction $\frac{16\left(-25\right)}{3\times 3}$.

$$\frac{-400}{9}$$

Fraction $\frac{-400}{9}$ can be rewritten as $-\frac{400}{9}$ by extracting the negative sign.

$$-\frac{400}{9}$$

Show Solution

Factor

$-\frac{400}{9} = -44\frac{4}{9} = -44.44444444444444$

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