What is -3+1+2\times (2-1/2+3) ?

The solution to -3+1+2\times (2-1/2+3) is 7

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-3+1+2\times (2-1/2+3)

- 3 + 1 + 2 \cdot (2 - \frac{1}{2} + 3)

7

Solution steps

- 3 + 1 + 2 (2 - \frac{1}{2} + 3)

Follow the PEMDAS order of operations

Calculate within parentheses

(2 - \frac{1}{2} + 3) : \frac{9}{2}

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

Add and subtract (left to right)

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

2 - \frac{1}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 2 - 1 = 3

2 \cdot 2 - 1

Multiply the numbers:

2 \cdot 2 = 4

= 4 - 1

Subtract the numbers:

4 - 1 = 3

= 3

= \frac{3}{2}

= \frac{3}{2} + 3

\frac{3}{2} + 3 = \frac{9}{2}

\frac{3}{2} + 3

Convert element to fraction:

3 = \frac{3 \cdot 2}{2}

= \frac{3 \cdot 2}{2} + \frac{3}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 2 + 3}{2}

3 \cdot 2 + 3 = 9

3 \cdot 2 + 3

Multiply the numbers:

3 \cdot 2 = 6

= 6 + 3

Add the numbers:

6 + 3 = 9

= 9

= \frac{9}{2}

= \frac{9}{2}

= - 3 + 1 + 2 \cdot \frac{9}{2}

Multiply and divide (left to right)

2 \cdot \frac{9}{2} : 9

2 \cdot \frac{9}{2}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{9}{2}

Cross-cancel common factor:

2

= \frac{9}{1}

Divide the numbers:

\frac{9}{1} = 9

= 9

= - 3 + 1 + 9

Add and subtract (left to right)

- 3 + 1 + 9 : 7

- 3 + 1 + 9

- 3 + 1 = - 2

= - 2 + 9

- 2 + 9 = 7

= 7

= 7

(- 5 - 4 + 11) + (- 18 + 12 - 6)

4 (5)^{2} - 8

4 (5)^{2} + 4

22 \cdot 1 0^{2}

18 \div (- 9) + 40 \div 8 - 5 \times 11