What is 4[8+4/67-20] ?

The solution to 4[8+4/67-20] is -3200/67

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4[8+4/67-20]

4 [8 + 4/67 - 20]

- \frac{3200}{67}

Solution steps

4 [8 + 4/67 - 20]

Follow the PEMDAS order of operations

Calculate within parentheses

[8 + 4/67 - 20] : - \frac{800}{67}

8 + 4/67 - 20

Multiply and divide (left to right)

4/67 : \frac{4}{67}

4/67

4/67 = \frac{4}{67}

= \frac{4}{67}

= 8 + \frac{4}{67} - 20

Add and subtract (left to right)

8 + \frac{4}{67} - 20 : - \frac{800}{67}

8 + \frac{4}{67} - 20

8 + \frac{4}{67} = \frac{540}{67}

8 + \frac{4}{67}

Convert element to fraction:

8 = \frac{8 \cdot 67}{67}

= \frac{8 \cdot 67}{67} + \frac{4}{67}

Since the denominators are equal, combine the fractions:

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

= \frac{8 \cdot 67 + 4}{67}

8 \cdot 67 + 4 = 540

8 \cdot 67 + 4

Multiply the numbers:

8 \cdot 67 = 536

= 536 + 4

Add the numbers:

536 + 4 = 540

= 540

= \frac{540}{67}

= \frac{540}{67} - 20

\frac{540}{67} - 20 = - \frac{800}{67}

\frac{540}{67} - 20

Convert element to fraction:

20 = \frac{20 \cdot 67}{67}

= - \frac{20 \cdot 67}{67} + \frac{540}{67}

Since the denominators are equal, combine the fractions:

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

= \frac{- 20 \cdot 67 + 540}{67}

- 20 \cdot 67 + 540 = - 800

- 20 \cdot 67 + 540

Multiply the numbers:

20 \cdot 67 = 1340

= - 1340 + 540

Add/Subtract the numbers:

- 1340 + 540 = - 800

= - 800

= \frac{- 800}{67}

Apply the fraction rule:

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

= - \frac{800}{67}

= - \frac{800}{67}

= - \frac{800}{67}

= 4 (- \frac{800}{67})

Multiply and divide (left to right)

4 (- \frac{800}{67}) : - \frac{3200}{67}

4 (- \frac{800}{67})

Apply rule

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

4 (- \frac{800}{67}) = - 4 \cdot \frac{800}{67}

Convert element to fraction:

4 = \frac{4}{1}

= - \frac{4}{1} \cdot \frac{800}{67}

Apply the fraction rule:

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

\frac{4}{1} \cdot \frac{800}{67} = \frac{4 \cdot 800}{1 \cdot 67}

= - \frac{4 \cdot 800}{1 \cdot 67}

Multiply the numbers:

4 \cdot 800 = 3200

= - \frac{3200}{1 \cdot 67}

Multiply the numbers:

1 \cdot 67 = 67

= - \frac{3200}{67}

= - \frac{3200}{67}

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