Step 1.
Convert 2\frac{5}{6}265 to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}acb=cac+b
\frac{15}{9}\div -\frac{2}{3}-\frac{2\times 6+5}{6}915÷−32−62×6+5
Step 2. Simplify 2\times 62×6 to 1212
\frac{15}{9}\div -\frac{2}{3}-\frac{12+5}{6}915÷−32−612+5
Step 3. Simplify 12+512+5 to 1717
\frac{15}{9}\div -\frac{2}{3}-\frac{17}{6}915÷−32−617
Step 4. Simplify \frac{15}{9}915 to \frac{5}{3}35
\frac{5}{3}\div -\frac{2}{3}-\frac{17}{6}35÷−32−617
Step 5. Apply this rule: a\div \frac{b}{c}=a\times \frac{c}{b}a÷cb=a×bc
\frac{5}{3}\times \frac{3}{-2}-\frac{17}{6}35×−23−617
Step 6. Apply this rule: \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}ba×dc=bdac
\frac{5\times 3}{3\times -2}-\frac{17}{6}3×−25×3−617
Step 7. Simplify 5\times 35×3 to 1515
\frac{15}{3\times -2}-\frac{17}{6}3×−215−617
Step 8. Simplify 3\times -23×−2 to -6−6
\frac{15}{-6}-\frac{17}{6}−615−617
Step 9. Move the negative sign to the left
-\frac{15}{6}-\frac{17}{6}−615−617
Step 10. Simplify \frac{15}{6}615 to \frac{5}{2}25
-\frac{5}{2}-\frac{17}{6}−25−617
Step 11. Find the Least Common Denominator (LCD) of \frac{5}{2}, \frac{17}{6}25,617
Method 1: By Listing MultiplesList out all multiples of each denominator, and find the first common one.Multiples of 2 : 2, 4, 6, ...
Multiples of 6 : 6, ...
Therefore, the LCD is 66.Method 2: By Prime FactorsList all prime factors of each denominator, and find the union of these primes.Prime Factors of 2 : 2
Prime Factors of 6 : 2, 3
Therefore, the LCD is 2\times 3=62×3=6.LCD = 66
Step 12. Make the denominators the same as the LCD
-\frac{5\times 3}{2\times 3}-\frac{17}{6}−2×35×3−617
Step 13. Simplify. Denominators are now the same
-\frac{15}{6}-\frac{17}{6}−615−617
Step. 14 Join the denominators
\frac{-15-17}{6}6−15−17
Step 15. Simplify
-\frac{32}{6}−632
Step. 16 Simplify \frac{32}{6}632 to \frac{16}{3}316
-\frac{16}{3}−316
Step 17. Convert to mixed fraction
-5\frac{1}{3}−531
Done your answer is [tex]-5 \frac{1}{3} [/tex]
