Question

1. add or subtract the mixed numbers. -8\frac{1}{3}-(-2\frac{1}{6}) -6\frac{1}{6} 6\frac{1}{3} 10\frac{1}{2} -10\frac{1}{9}

Explanation:

Step1: Convert mixed - numbers to improper fractions

$-8\frac{1}{3}=-\frac{8\times3 + 1}{3}=-\frac{25}{3}$ and $-2\frac{1}{6}=-\frac{2\times6+1}{6}=-\frac{13}{6}$
The expression becomes $-\frac{25}{3}-(-\frac{13}{6})$.

Step2: Simplify the double - negative

$-\frac{25}{3}-(-\frac{13}{6})=-\frac{25}{3}+\frac{13}{6}$

Step3: Find a common denominator

The common denominator of 3 and 6 is 6. So $-\frac{25}{3}=-\frac{25\times2}{3\times2}=-\frac{50}{6}$
The expression is now $-\frac{50}{6}+\frac{13}{6}$

Step4: Add the fractions

$-\frac{50}{6}+\frac{13}{6}=\frac{-50 + 13}{6}=-\frac{37}{6}$

Step5: Convert back to a mixed number

$-\frac{37}{6}=-6\frac{1}{6}$

Answer:

$-6\frac{1}{6}$