What is (2+7 1/3)+(2/3-4)+3 ?

The solution to (2+7 1/3)+(2/3-4)+3 is 9

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(2+7 1/3)+(2/3-4)+3

(2 + 7 \frac{1}{3}) + (\frac{2}{3} - 4) + 3

9

Solution steps

(2 + 7 \frac{1}{3}) + (\frac{2}{3} - 4) + 3

Convert mixed numbers to improper fractions:

7 \frac{1}{3} = \frac{22}{3}

7 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

7 \frac{1}{3} = \frac{7 \cdot 3 + 1}{3}

= \frac{22}{3}

= (2 + \frac{22}{3}) + (\frac{2}{3} - 4) + 3

Follow the PEMDAS order of operations

Calculate within parentheses

(2 + \frac{22}{3}) : \frac{28}{3}

2 + \frac{22}{3}

2 + \frac{22}{3} = \frac{28}{3}

2 + \frac{22}{3}

Convert element to fraction:

2 = \frac{2 \cdot 3}{3}

= \frac{2 \cdot 3}{3} + \frac{22}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 3 + 22}{3}

2 \cdot 3 + 22 = 28

2 \cdot 3 + 22

Multiply the numbers:

2 \cdot 3 = 6

= 6 + 22

Add the numbers:

6 + 22 = 28

= 28

= \frac{28}{3}

= \frac{28}{3}

= \frac{28}{3} + (\frac{2}{3} - 4) + 3

Calculate within parentheses

(\frac{2}{3} - 4) : - \frac{10}{3}

\frac{2}{3} - 4

\frac{2}{3} - 4 = - \frac{10}{3}

\frac{2}{3} - 4

Convert element to fraction:

4 = \frac{4 \cdot 3}{3}

= - \frac{4 \cdot 3}{3} + \frac{2}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 4 \cdot 3 + 2}{3}

- 4 \cdot 3 + 2 = - 10

- 4 \cdot 3 + 2

Multiply the numbers:

4 \cdot 3 = 12

= - 12 + 2

Add/Subtract the numbers:

- 12 + 2 = - 10

= - 10

= \frac{- 10}{3}

Apply the fraction rule:

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

= - \frac{10}{3}

= - \frac{10}{3}

= \frac{28}{3} - \frac{10}{3} + 3

Add and subtract (left to right)

\frac{28}{3} - \frac{10}{3} + 3 : 9

\frac{28}{3} - \frac{10}{3} + 3

\frac{28}{3} - \frac{10}{3} = 6

\frac{28}{3} - \frac{10}{3}

Apply rule

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

= \frac{28 - 10}{3}

Subtract the numbers:

28 - 10 = 18

= \frac{18}{3}

Divide the numbers:

\frac{18}{3} = 6

= 6

= 6 + 3

6 + 3 = 9

= 9

= 9

2 (- 3)^{1} + 5^{1}

- 77 + [- 56 - 65 - 54 + (- 8)]

21 - [- (3 - 4) - 3] - 5

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

310 \div 5 \times 16 + 240 \div 6 \times 5