What is 8/3-7+20/3-12 ?

The solution to 8/3-7+20/3-12 is -29/3

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8/3-7+20/3-12

\frac{8}{3} - 7 + \frac{20}{3} - 12

- \frac{29}{3}

Solution steps

\frac{8}{3} - 7 + \frac{20}{3} - 12

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{8}{3} - 7 = - \frac{13}{3}

\frac{8}{3} - 7

Convert element to fraction:

7 = \frac{7 \cdot 3}{3}

= - \frac{7 \cdot 3}{3} + \frac{8}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 7 \cdot 3 + 8}{3}

- 7 \cdot 3 + 8 = - 13

- 7 \cdot 3 + 8

Multiply the numbers:

7 \cdot 3 = 21

= - 21 + 8

Add/Subtract the numbers:

- 21 + 8 = - 13

= - 13

= \frac{- 13}{3}

Apply the fraction rule:

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

= - \frac{13}{3}

= - \frac{13}{3} + \frac{20}{3} - 12

- \frac{13}{3} + \frac{20}{3} = \frac{7}{3}

- \frac{13}{3} + \frac{20}{3}

Apply rule

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

= \frac{- 13 + 20}{3}

Add/Subtract the numbers:

- 13 + 20 = 7

= \frac{7}{3}

= \frac{7}{3} - 12

\frac{7}{3} - 12 = - \frac{29}{3}

\frac{7}{3} - 12

Convert element to fraction:

12 = \frac{12 \cdot 3}{3}

= - \frac{12 \cdot 3}{3} + \frac{7}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 12 \cdot 3 + 7}{3}

- 12 \cdot 3 + 7 = - 29

- 12 \cdot 3 + 7

Multiply the numbers:

12 \cdot 3 = 36

= - 36 + 7

Add/Subtract the numbers:

- 36 + 7 = - 29

= - 29

= \frac{- 29}{3}

Apply the fraction rule:

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

= - \frac{29}{3}

= - \frac{29}{3}

- 3 (2) + 6

5 (8 + 6)

- 4^{2} + 4

- 4^{2} + 5

- 4^{2} + 1