What is 8-(-2 2/3)+7-(-1 1/3)+5 ?

The solution to 8-(-2 2/3)+7-(-1 1/3)+5 is 24

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8-(-2 2/3)+7-(-1 1/3)+5

8 - (- 2 \frac{2}{3}) + 7 - (- 1 \frac{1}{3}) + 5

24

Solution steps

8 - (- 2 \frac{2}{3}) + 7 - (- 1 \frac{1}{3}) + 5

Convert mixed numbers to improper fractions:

2 \frac{2}{3} = \frac{8}{3}

2 \frac{2}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{8}{3}

= 8 - (- \frac{8}{3}) + 7 - (- 1 \frac{1}{3}) + 5

Convert mixed numbers to improper fractions:

1 \frac{1}{3} = \frac{4}{3}

1 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{4}{3}

= 8 - (- \frac{8}{3}) + 7 - (- \frac{4}{3}) + 5

Follow the PEMDAS order of operations

Add and subtract (left to right)

8 - (- \frac{8}{3}) + 7 - (- \frac{4}{3}) + 5 : 24

8 - (- \frac{8}{3}) + 7 - (- \frac{4}{3}) + 5

Apply rule

- (- a) = + a

- (- \frac{8}{3}) = + \frac{8}{3}

= 8 + \frac{8}{3} + 7 - (- \frac{4}{3}) + 5

8 + \frac{8}{3} = \frac{32}{3}

8 + \frac{8}{3}

Convert element to fraction:

8 = \frac{8 \cdot 3}{3}

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

8 \cdot 3 + 8 = 32

8 \cdot 3 + 8

Multiply the numbers:

8 \cdot 3 = 24

= 24 + 8

Add the numbers:

24 + 8 = 32

= 32

= \frac{32}{3}

= \frac{32}{3} + 7 - (- \frac{4}{3}) + 5

\frac{32}{3} + 7 = \frac{53}{3}

\frac{32}{3} + 7

Convert element to fraction:

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

= \frac{7 \cdot 3}{3} + \frac{32}{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 + 32}{3}

7 \cdot 3 + 32 = 53

7 \cdot 3 + 32

Multiply the numbers:

7 \cdot 3 = 21

= 21 + 32

Add the numbers:

21 + 32 = 53

= 53

= \frac{53}{3}

= \frac{53}{3} - (- \frac{4}{3}) + 5

Apply rule

- (- a) = + a

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

= \frac{53}{3} + \frac{4}{3} + 5

\frac{53}{3} + \frac{4}{3} = 19

\frac{53}{3} + \frac{4}{3}

Apply rule

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

= \frac{53 + 4}{3}

Add the numbers:

53 + 4 = 57

= \frac{57}{3}

Divide the numbers:

\frac{57}{3} = 19

= 19

= 19 + 5

19 + 5 = 24

= 24

= 24

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