\[\frac{-5}{9}+\frac{\frac{5}{9}}{1\frac{2}{3}-2\frac{1}{12}}\]
1
Convert 1231\frac{2}{3} to improper fraction. Use this rule: abc=ac+bca \frac{b}{c}=\frac{ac+b}{c}.
−59+591×3+23−2112\frac{-5}{9}+\frac{\frac{5}{9}}{\frac{1\times 3+2}{3}-2\frac{1}{12}}

2
Simplify  1×31\times 3  to  33.
−59+593+23−2112\frac{-5}{9}+\frac{\frac{5}{9}}{\frac{3+2}{3}-2\frac{1}{12}}

3
Simplify  3+23+2  to  55.
−59+5953−2112\frac{-5}{9}+\frac{\frac{5}{9}}{\frac{5}{3}-2\frac{1}{12}}

4
Convert 21122\frac{1}{12} to improper fraction. Use this rule: abc=ac+bca \frac{b}{c}=\frac{ac+b}{c}.
−59+5953−2×12+112\frac{-5}{9}+\frac{\frac{5}{9}}{\frac{5}{3}-\frac{2\times 12+1}{12}}

5
Simplify  2×122\times 12  to  2424.
−59+5953−24+112\frac{-5}{9}+\frac{\frac{5}{9}}{\frac{5}{3}-\frac{24+1}{12}}

6
Simplify  24+124+1  to  2525.
−59+5953−2512\frac{-5}{9}+\frac{\frac{5}{9}}{\frac{5}{3}-\frac{25}{12}}

7
Find the Least Common Denominator (LCD) of 53,2512\frac{5}{3},\frac{25}{12}. In other words, find the Least Common Multiple (LCM) of 3,123,12.
LCD = 1212

8
Make the denominators the same as the LCD.
5×43×4−2512\frac{5\times 4}{3\times 4}-\frac{25}{12}

9
Simplify. Denominators are now the same.
2012−2512\frac{20}{12}-\frac{25}{12}

10
Join the denominators.
20−2512\frac{20-25}{12}

11
Simplify  53−2512\frac{5}{3}-\frac{25}{12}  to  −512-\frac{5}{12}.
−59+59−512\frac{-5}{9}+\frac{\frac{5}{9}}{-\frac{5}{12}}

12
Move the negative sign to the left.
−59+59−512-\frac{5}{9}+\frac{\frac{5}{9}}{-\frac{5}{12}}

13
Invert and multiply.
−59+59×−125-\frac{5}{9}+\frac{5}{9}\times \frac{-12}{5}

14
Cancel 55.
−59+19×−12-\frac{5}{9}+\frac{1}{9}\times -12

15
Move the negative sign to the left.
−59−129-\frac{5}{9}-\frac{12}{9}

16
Simplify  129\frac{12}{9}  to  43\frac{4}{3}.
−59−43-\frac{5}{9}-\frac{4}{3}

17
Find the Least Common Denominator (LCD) of 59,43\frac{5}{9},\frac{4}{3}. In other words, find the Least Common Multiple (LCM) of 9,39,3.
LCD = 99

18
Make the denominators the same as the LCD.
−59−4×33×3-\frac{5}{9}-\frac{4\times 3}{3\times 3}

19
Simplify. Denominators are now the same.
−59−129-\frac{5}{9}-\frac{12}{9}

20
Join the denominators.
−5−129\frac{-5-12}{9}

21
Simplify.
−179-\frac{17}{9}

22
Convert to mixed fraction.
−189-1\frac{8}{9}

Done

Decimal Form: -1.888889
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