What is 1/4 (-3)^2-5 ?

The solution to 1/4 (-3)^2-5 is -11/4

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1/4 (-3)^2-5

\frac{1}{4} (- 3)^{2} - 5

- \frac{11}{4}

Solution steps

\frac{1}{4} (- 3)^{2} - 5

Follow the PEMDAS order of operations

Calculate exponents

(- 3)^{2} : 9

(- 3)^{2}

Apply exponent rule:

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

n

is even

(- 3)^{2} = 3^{2} = 9

= 9

= \frac{1}{4} \cdot 9 - 5

Multiply and divide (left to right)

\frac{1}{4} \cdot 9 : \frac{9}{4}

\frac{1}{4} \cdot 9

Convert element to fraction:

9 = \frac{9}{1}

= \frac{1}{4} \cdot \frac{9}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 9}{4 \cdot 1}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{9}{4 \cdot 1}

Multiply the numbers:

4 \cdot 1 = 4

= \frac{9}{4}

= \frac{9}{4} - 5

Add and subtract (left to right)

\frac{9}{4} - 5 : - \frac{11}{4}

\frac{9}{4} - 5

\frac{9}{4} - 5 = - \frac{11}{4}

\frac{9}{4} - 5

Convert element to fraction:

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

= - \frac{5 \cdot 4}{4} + \frac{9}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{- 5 \cdot 4 + 9}{4}

- 5 \cdot 4 + 9 = - 11

- 5 \cdot 4 + 9

Multiply the numbers:

5 \cdot 4 = 20

= - 20 + 9

Add/Subtract the numbers:

- 20 + 9 = - 11

= - 11

= \frac{- 11}{4}

Apply the fraction rule:

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

= - \frac{11}{4}

= - \frac{11}{4}

= - \frac{11}{4}

3 (- 3) + 9

9 \div 3 (1 + 2)

8 \div 4 (2 + 2)

152 \div (32 - 8 \times 3) \times 5

(- 32 + 29 - 10) - 12 - 4 + (27 - 38)