What is 2+1/2-[1-(1/2+1)] ?

The solution to 2+1/2-[1-(1/2+1)] is 3

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Popular >

2+1/2-[1-(1/2+1)]

Solution

2 + \frac{1}{2} - [1 - (\frac{1}{2} + 1)]

Solution

3

Solution steps

2 + \frac{1}{2} - [1 - (\frac{1}{2} + 1)]

Follow the PEMDAS order of operations

Calculate within parentheses

[1 - (\frac{1}{2} + 1)] : - \frac{1}{2}

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

Calculate within parentheses

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

\frac{1}{2} + 1

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

\frac{1}{2} + 1

Convert element to fraction:

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

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

1 \cdot 2 + 1 = 3

1 \cdot 2 + 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 + 1

Add the numbers:

2 + 1 = 3

= 3

= \frac{3}{2}

= \frac{3}{2}

= 1 - \frac{3}{2}

Add and subtract (left to right)

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

1 - \frac{3}{2}

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

1 - \frac{3}{2}

Convert element to fraction:

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

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

1 \cdot 2 - 3 = - 1

1 \cdot 2 - 3

Multiply the numbers:

1 \cdot 2 = 2

= 2 - 3

Subtract the numbers:

2 - 3 = - 1

= - 1

= \frac{- 1}{2}

Apply the fraction rule:

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

= - \frac{1}{2}

= - \frac{1}{2}

= - \frac{1}{2}

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

Add and subtract (left to right)

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

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

2 + \frac{1}{2} = \frac{5}{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 = 5

2 \cdot 2 + 1

Multiply the numbers:

2 \cdot 2 = 4

= 4 + 1

Add the numbers:

4 + 1 = 5

= 5

= \frac{5}{2}

= \frac{5}{2} - (- \frac{1}{2})

Apply rule

- (- a) = + a

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

= \frac{5}{2} + \frac{1}{2}

\frac{5}{2} + \frac{1}{2} = 3

\frac{5}{2} + \frac{1}{2}

Apply rule

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

= \frac{5 + 1}{2}

Add the numbers:

5 + 1 = 6

= \frac{6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3

= 3

= 3

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Frequently Asked Questions (FAQ)

What is 2+1/2-[1-(1/2+1)] ?
The solution to 2+1/2-[1-(1/2+1)] is 3