Question

15/9 divided by (-2/3) + (-2 5/6)

Answer 1

Step 1.
Convert 2\frac{5}{6}2​6​​5​​ to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a​c​​b​​=​c​​ac+b​​
\frac{15}{9}\div -\frac{2}{3}-\frac{2\times 6+5}{6}​9​​15​​÷−​3​​2​​−​6​​2×6+5​​
Step 2. Simplify 2\times 62×6 to 1212
\frac{15}{9}\div -\frac{2}{3}-\frac{12+5}{6}​9​​15​​÷−​3​​2​​−​6​​12+5​​
Step 3. Simplify 12+512+5 to 1717
\frac{15}{9}\div -\frac{2}{3}-\frac{17}{6}​9​​15​​÷−​3​​2​​−​6​​17​​
Step 4. Simplify \frac{15}{9}​9​​15​​ to \frac{5}{3}​3​​5​​
\frac{5}{3}\div -\frac{2}{3}-\frac{17}{6}​3​​5​​÷−​3​​2​​−​6​​17​​
Step 5. Apply this rule: a\div \frac{b}{c}=a\times \frac{c}{b}a÷​c​​b​​=a×​b​​c​​
\frac{5}{3}\times \frac{3}{-2}-\frac{17}{6}​3​​5​​×​−2​​3​​−​6​​17​​
Step 6. Apply this rule: \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}​b​​a​​×​d​​c​​=​bd​​ac​​
\frac{5\times 3}{3\times -2}-\frac{17}{6}​3×−2​​5×3​​−​6​​17​​
Step 7. Simplify 5\times 35×3 to 1515
\frac{15}{3\times -2}-\frac{17}{6}​3×−2​​15​​−​6​​17​​
Step 8. Simplify 3\times -23×−2 to -6−6
\frac{15}{-6}-\frac{17}{6}​−6​​15​​−​6​​17​​
Step 9. Move the negative sign to the left
-\frac{15}{6}-\frac{17}{6}−​6​​15​​−​6​​17​​
Step 10. Simplify \frac{15}{6}​6​​15​​ to \frac{5}{2}​2​​5​​
-\frac{5}{2}-\frac{17}{6}−​2​​5​​−​6​​17​​
Step 11. Find the Least Common Denominator (LCD) of \frac{5}{2}, \frac{17}{6}​2​​5​​,​6​​17​​
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}−​2×3​​5×3​​−​6​​17​​
Step 13. Simplify. Denominators are now the same
-\frac{15}{6}-\frac{17}{6}−​6​​15​​−​6​​17​​
Step. 14 Join the denominators
\frac{-15-17}{6}​6​​−15−17​​
Step 15. Simplify
-\frac{32}{6}−​6​​32​​
Step. 16 Simplify \frac{32}{6}​6​​32​​ to \frac{16}{3}​3​​16​​
-\frac{16}{3}−​3​​16​​
Step 17. Convert to mixed fraction
-5\frac{1}{3}−5​3​​1​​
Done your answer is
`-5 (1)/(3)`