What is -1/4 (-5)^2+4 ?

The solution to -1/4 (-5)^2+4 is -9/4

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-1/4 (-5)^2+4

- \frac{1}{4} (- 5)^{2} + 4

- \frac{9}{4}

Solution steps

- \frac{1}{4} (- 5)^{2} + 4

Follow the PEMDAS order of operations

Calculate exponents

(- 5)^{2} : 25

(- 5)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 5)^{2} = 5^{2} = 25

= 25

= - \frac{1}{4} \cdot 25 + 4

Multiply and divide (left to right)

- \frac{1}{4} \cdot 25 : - \frac{25}{4}

- \frac{1}{4} \cdot 25

Convert element to fraction:

25 = \frac{25}{1}

= - \frac{1}{4} \cdot \frac{25}{1}

Apply the fraction rule:

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

\frac{1}{4} \cdot \frac{25}{1} = \frac{1 \cdot 25}{4 \cdot 1}

= - \frac{1 \cdot 25}{4 \cdot 1}

Multiply the numbers:

1 \cdot 25 = 25

= - \frac{25}{4 \cdot 1}

Multiply the numbers:

4 \cdot 1 = 4

= - \frac{25}{4}

= - \frac{25}{4} + 4

Add and subtract (left to right)

- \frac{25}{4} + 4 : - \frac{9}{4}

- \frac{25}{4} + 4

- \frac{25}{4} + 4 = - \frac{9}{4}

- \frac{25}{4} + 4

Convert element to fraction:

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

= \frac{4 \cdot 4}{4} - \frac{25}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{4 \cdot 4 - 25}{4}

4 \cdot 4 - 25 = - 9

4 \cdot 4 - 25

Multiply the numbers:

4 \cdot 4 = 16

= 16 - 25

Subtract the numbers:

16 - 25 = - 9

= - 9

= \frac{- 9}{4}

Apply the fraction rule:

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

= - \frac{9}{4}

= - \frac{9}{4}

= - \frac{9}{4}

\frac{180 ( 5 - 2 )}{5}

- 12 + 7 - 9 \cdot 3

6 (- 4)^{2}

5 - (- 2) + (- 8) \div (- 4) - 5

6 \cdot 2^{5}