The solution to 1/3-1^2 is -2/3

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1/3-1^2

Solution

\frac{1}{3} - 1^{2}

- \frac{2}{3}

Solution steps

\frac{1}{3} - 1^{2}

Follow the PEMDAS order of operations

Calculate exponents

1^{2} : 1

1^{2}

1^{2} = 1

= 1

= \frac{1}{3} - 1

Add and subtract (left to right)

\frac{1}{3} - 1 : - \frac{2}{3}

\frac{1}{3} - 1

\frac{1}{3} - 1 = - \frac{2}{3}

\frac{1}{3} - 1

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

= - \frac{1 \cdot 3}{3} + \frac{1}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 1 \cdot 3 + 1}{3}

- 1 \cdot 3 + 1 = - 2

- 1 \cdot 3 + 1

Multiply the numbers:

1 \cdot 3 = 3

= - 3 + 1

Add/Subtract the numbers:

- 3 + 1 = - 2

= - 2

= \frac{- 2}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{3}

= - \frac{2}{3}

= - \frac{2}{3}

22 \div 2 \times 3^{2}

5 (- 2) + 1

(- 3)^{4} + (- 5)^{2}

1 0^{100} - 2011

(120 \div 20) \div (2 \times 3)