What is -1/4 (-2)^2-5/8 (-2) ?

The solution to -1/4 (-2)^2-5/8 (-2) is 1/4

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-1/4 (-2)^2-5/8 (-2)

- \frac{1}{4} (- 2)^{2} - \frac{5}{8} (- 2)

\frac{1}{4}

Solution steps

- \frac{1}{4} (- 2)^{2} - \frac{5}{8} (- 2)

Follow the PEMDAS order of operations

Calculate exponents

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

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

n

is even

(- 2)^{2} = 2^{2} = 4

= 4

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

Multiply and divide (left to right)

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

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

Convert element to fraction:

4 = \frac{4}{1}

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

Cross-cancel common factor:

4

= - 1

= - 1 - \frac{5}{8} (- 2)

Multiply and divide (left to right)

\frac{5}{8} (- 2) : - \frac{5}{4}

\frac{5}{8} (- 2)

Apply rule

a \cdot (- b) = - a \cdot b

\frac{5}{8} (- 2) = - \frac{5}{8} \cdot 2

Convert element to fraction:

2 = \frac{2}{1}

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

Apply the fraction rule:

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

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

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

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

\frac{5 \cdot 2}{8 \cdot 1}

Multiply the numbers:

8 \cdot 1 = 8

= \frac{5 \cdot 2}{8}

Factor the number:

8 = 2 \cdot 4

= \frac{5 \cdot 2}{2 \cdot 4}

Cancel the common factor:

2

= \frac{5}{4}

= - \frac{5}{4}

= - 1 - (- \frac{5}{4})

Add and subtract (left to right)

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

- 1 - (- \frac{5}{4})

Apply rule

- (- a) = + a

- (- \frac{5}{4}) = + \frac{5}{4}

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

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

= \frac{1}{4}

= \frac{1}{4}

31/4 \times 6/8

(- 2)^{4} - 15 (- 2)^{2} + 10 (- 2) + 24

\frac{3 ^{2} \cdot 2 ^{4}}{6 ^{6}}

- 2 \div 3 (- 3)

- 9 + {- 5 [- 7 - (- 3 \cdot 4)] + 6} - 4