Answer:
Part 1) [tex]-17\frac{8}{9}[/tex] -----> [tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]
Part 2) [tex]-15.11[/tex] ------> [tex]-12.48-(-2.99)-5.62[/tex]
Part 3) [tex]-19\frac{8}{9}[/tex] -----> [tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]
Part 4) [tex]-201.65[/tex] -----> [tex]-353.92-(-283.56)-131.29[/tex]
Part 5) [tex]74[/tex] ------> [tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]
Step-by-step explanation:
Part 1) we have
[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]
To calculate the subtraction convert the mixed numbers to an improper fractions
[tex]6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}[/tex]
[tex]3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}[/tex]
[tex]8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}[/tex]
substitute
[tex]-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}[/tex]
Convert to mixed number
[tex]-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}[/tex]
Part 2) we have
[tex]-12.48-(-2.99)-5.62[/tex]
To calculate the subtraction eliminate the parenthesis first
[tex]-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11[/tex]
Part 3) we have
[tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]
To calculate the subtraction convert the mixed numbers to an improper fractions
[tex]19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}[/tex]
[tex]4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}[/tex]
[tex]3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}[/tex]
substitute
[tex]-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})[/tex]
Eliminate the parenthesis
[tex]-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}[/tex]
Convert to mixed number
[tex]-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}[/tex]
Part 4) we have
[tex]-353.92-(-283.56)-131.29[/tex]
To calculate the subtraction eliminate the parenthesis first
[tex]-353.92+283.56-131.29=-201.65[/tex]
Part 5) we have
[tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]
To calculate the subtraction convert the mixed numbers to an improper fractions
[tex]83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}[/tex]
[tex]108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}[/tex]
[tex]99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}[/tex]
substitute
[tex]\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})[/tex]
Eliminate the parenthesis
[tex]\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74[/tex]
