- 9 + 12 x (-1/3)+2÷1/9=

5

Step-by-step explanation:

Multiply

( −9 ) + 12× (- 1/3) + 2 ÷ 1/9 = ( −9 ) + (-12/3) + 2 ÷ 1/9  

−1/3 × 12 = − 1 × 12 /3 = −12/3

Divide

( −9 ) + (−12/3) + 2 ÷ 1/9 = ( −9 ) + (-12/3) + 18/1  

Convert integer to fraction

2 = 2/1  

2/1 ÷ 1/9 = 2/1  × 9 over 1 = ( 2 × 9 ) over ( 1 × 1 ) = 18/1

To divide fractions, invert the second one (turn it upside-down), then multiply the numerators and denominators.

Add

( −9 ) + (−12/3) + 18/1  = (−39/3 ) + 18/1  

Convert integer to fraction

−9 = -9/1  

Add a negative

-9/1 + (12/ 3) = -9/1 − 12 over 3

Adding a negative is the same as subtracting a positive.  

Find common denominator  

-9/1  − 12/3 = −( 9 × 3 ) / ( 1 × 3 )  - (12 × 1 ) / ( 3 × 1 ) = -27/3 − 12/3

3 is the least common multiple of denominators 1 and 3. Use it to convert to equivalent fractions with this common denominator.

Subtract  

-27/3 − 12/3 = (- 27−27 − 12 )/3 = −39/3  

Add

(-39/3) + 18/1 = 15/3

Find common denominator

−39/3 + 18/1 = −( 39 × 1 ) / ( 3 × 1 ) + ( 18 × 3 ) / ( 1 × 3 )  = -39/3 + 54/3

3 is the least common multiple of denominators 3 and 1. Use it to convert to equivalent fractions with this common denominator.  

Add

-39/3 + 54/3 = ( -39−39 + 54 ) /3 = 15 over 3

Simplify

15/3 = 5

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