What is 1/2-8(1/4+1) ?

The solution to 1/2-8(1/4+1) is -19/2

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1/2-8(1/4+1)

\frac{1}{2} - 8 (\frac{1}{4} + 1)

- \frac{19}{2}

Solution steps

\frac{1}{2} - 8 (\frac{1}{4} + 1)

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{4} + 1) : \frac{5}{4}

\frac{1}{4} + 1

\frac{1}{4} + 1 = \frac{5}{4}

\frac{1}{4} + 1

Convert element to fraction:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} + \frac{1}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 4 + 1}{4}

1 \cdot 4 + 1 = 5

1 \cdot 4 + 1

Multiply the numbers:

1 \cdot 4 = 4

= 4 + 1

Add the numbers:

4 + 1 = 5

= 5

= \frac{5}{4}

= \frac{5}{4}

= \frac{1}{2} - 8 \cdot \frac{5}{4}

Multiply and divide (left to right)

8 \cdot \frac{5}{4} : 10

8 \cdot \frac{5}{4}

Convert element to fraction:

8 = \frac{8}{1}

= \frac{8}{1} \cdot \frac{5}{4}

Apply the fraction rule:

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

= \frac{8 \cdot 5}{1 \cdot 4}

Cancel

\frac{8 \cdot 5}{1 \cdot 4} : 10

\frac{8 \cdot 5}{1 \cdot 4}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{8 \cdot 5}{4}

Divide the numbers:

\frac{8}{4} = 2

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

= 10

= \frac{1}{2} - 10

Add and subtract (left to right)

\frac{1}{2} - 10 : - \frac{19}{2}

\frac{1}{2} - 10

\frac{1}{2} - 10 = - \frac{19}{2}

\frac{1}{2} - 10

Convert element to fraction:

10 = \frac{10 \cdot 2}{2}

= - \frac{10 \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{- 10 \cdot 2 + 1}{2}

- 10 \cdot 2 + 1 = - 19

- 10 \cdot 2 + 1

Multiply the numbers:

10 \cdot 2 = 20

= - 20 + 1

Add/Subtract the numbers:

- 20 + 1 = - 19

= - 19

= \frac{- 19}{2}

Apply the fraction rule:

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

= - \frac{19}{2}

= - \frac{19}{2}

= - \frac{19}{2}

(1 + 2)^{2} + 14 \div 2 + 5

1^{2} + 2 (1) - 1

(\frac{7}{2} \div \frac{4}{4}) - \frac{3}{8}

\frac{2}{9} \times \frac{3}{4} \times (- 7)

- 18 + (- 6) - (+ 11) - (- 5 + 7)