Solve 1/3+2{-1+4/3[(-2+1-2)div(1+3)]+(4-3-7)}

$$\frac { 1 } { 3 } + 2 \{ - 1 + \frac { 4 } { 3 } [ ( - 2 + 1 - 2 ) \div ( 1 + 3 ) ] + ( 4 - 3 - 7 ) \}$$

Evaluate

$$-\frac{47}{3}\approx -15.666666667$$

Solution Steps

Add -2 and 1 to get -1.

$$\frac{1}{3}+2\left(-1+\frac{4}{3}\times \frac{-1-2}{1+3}+4-3-7\right)$$

Subtract 2 from -1 to get -3.

$$\frac{1}{3}+2\left(-1+\frac{4}{3}\times \frac{-3}{1+3}+4-3-7\right)$$

Add 1 and 3 to get 4.

$$\frac{1}{3}+2\left(-1+\frac{4}{3}\times \frac{-3}{4}+4-3-7\right)$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{1}{3}+2\left(-1+\frac{4}{3}\left(-\frac{3}{4}\right)+4-3-7\right)$$

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

$$\frac{1}{3}+2\left(-1+\frac{4\left(-3\right)}{3\times 4}+4-3-7\right)$$

Cancel out 4 in both numerator and denominator.

$$\frac{1}{3}+2\left(-1+\frac{-3}{3}+4-3-7\right)$$

Divide -3 by 3 to get -1.

$$\frac{1}{3}+2\left(-1-1+4-3-7\right)$$

Subtract 1 from -1 to get -2.

$$\frac{1}{3}+2\left(-2+4-3-7\right)$$

Add -2 and 4 to get 2.

$$\frac{1}{3}+2\left(2-3-7\right)$$

Subtract 3 from 2 to get -1.

$$\frac{1}{3}+2\left(-1-7\right)$$

Subtract 7 from -1 to get -8.

$$\frac{1}{3}+2\left(-8\right)$$

Multiply 2 and -8 to get -16.

$$\frac{1}{3}-16$$

Convert 16 to fraction \frac{48}{3}.

$$\frac{1}{3}-\frac{48}{3}$$

Since \frac{1}{3} and \frac{48}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-48}{3}$$

Subtract 48 from 1 to get -47.

$$-\frac{47}{3}$$

Factor

$$-\frac{47}{3} = -15\frac{2}{3} = -15.666666666666666$$