What is 1+(-1/2)(22-1) ?

The solution to 1+(-1/2)(22-1) is -19/2

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1+(-1/2)(22-1)

1 + (- \frac{1}{2}) (22 - 1)

- \frac{19}{2}

Solution steps

1 + (- \frac{1}{2}) (22 - 1)

Follow the PEMDAS order of operations

Calculate within parentheses

(22 - 1) : 21

22 - 1

22 - 1 = 21

= 21

= 1 + (- \frac{1}{2}) \cdot 21

Multiply and divide (left to right)

(- \frac{1}{2}) \cdot 21 : - \frac{21}{2}

(- \frac{1}{2}) \cdot 21

Apply rule

(- a) \cdot b = - a \cdot b

(- \frac{1}{2}) \cdot 21 = - \frac{1}{2} \cdot 21

Convert element to fraction:

21 = \frac{21}{1}

= - \frac{1}{2} \cdot \frac{21}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

\frac{1}{2} \cdot \frac{21}{1} = \frac{1 \cdot 21}{2 \cdot 1}

= - \frac{1 \cdot 21}{2 \cdot 1}

Multiply the numbers:

1 \cdot 21 = 21

= - \frac{21}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= - \frac{21}{2}

= 1 - \frac{21}{2}

Add and subtract (left to right)

1 - \frac{21}{2} : - \frac{19}{2}

1 - \frac{21}{2}

1 - \frac{21}{2} = - \frac{19}{2}

1 - \frac{21}{2}

Convert element to fraction:

1 = \frac{1 \cdot 2}{2}

= \frac{1 \cdot 2}{2} - \frac{21}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 2 - 21}{2}

1 \cdot 2 - 21 = - 19

1 \cdot 2 - 21

Multiply the numbers:

1 \cdot 2 = 2

= 2 - 21

Subtract the numbers:

2 - 21 = - 19

= - 19

= \frac{- 19}{2}

Apply the fraction rule:

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

= - \frac{19}{2}

= - \frac{19}{2}

= - \frac{19}{2}

5 \times (- 2 - 8)

- 6 + (- 9 + 2) - (- 2 - 1) + 4

4^{5} + 3^{5}

2 \cdot (- \frac{1}{2}) + 1

- 5 {4 + [3 - (4 - 8) + (- 5 - 10)]}