Question

1. $\frac{1}{6}div(-\frac{4}{5})$ a. $\frac{5}{24}$ b. $\frac{2}{15}$ c. $\frac{5}{24}$ d. $\frac{2}{15}$ 10. $-2\frac{2}{3}+\frac{4}{5}$ a. $-3\frac{1}{3}$ b. $-\frac{5}{6}$ c. $-2\frac{2}{15}$ d. $-2\frac{5}{6}$ 11. $-2 + 4\frac{4}{5}$ a. $\frac{5}{12}$ b. $-8\frac{4}{5}$ c. $-9\frac{3}{5}$ d. $\frac{10}{21}$ 12. $27div(-9)$ a. 18 b. 3 c. -3 d. -18 13. write $5\frac{1}{3}$ as an improper fraction. a. $\frac{13}{3}$ b. $\frac{11}{3}$ c. $\frac{17}{3}$ d. $\frac{16}{3}$ 14. $\frac{49}{8}$ a. $8\frac{1}{7}$ b. $6\frac{1}{8}$ c. $3\frac{1}{7}$ d. $3\frac{1}{8}$ write the improper fraction as a mixed number in simplest form.

Explanation:

Step1: Solve problem 9

To divide $\frac{1}{6}\div(-\frac{4}{5})$, use the rule of dividing fractions: $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$. So $\frac{1}{6}\div(-\frac{4}{5})=\frac{1}{6}\times(-\frac{5}{4})=-\frac{5}{24}$. There is an error in the options as the correct answer should be $-\frac{5}{24}$ and none of the given options match.

Step2: Solve problem 10

First, convert $- 2\frac{2}{3}$ to an improper fraction: $-2\frac{2}{3}=-\frac{2\times3 + 2}{3}=-\frac{8}{3}$. Then find a common - denominator for $-\frac{8}{3}+\frac{4}{5}$. The common denominator of 3 and 5 is 15. So $-\frac{8}{3}+\frac{4}{5}=-\frac{8\times5}{3\times5}+\frac{4\times3}{5\times3}=-\frac{40}{15}+\frac{12}{15}=-\frac{28}{15}=-1\frac{13}{15}=-2\frac{2}{15}$. The answer is C.

Step3: Solve problem 11

First, convert $4\frac{4}{5}$ to an improper fraction: $4\frac{4}{5}=\frac{4\times5 + 4}{5}=\frac{24}{5}$. Then $-2 + 4\frac{4}{5}=-2+\frac{24}{5}=\frac{-2\times5}{1\times5}+\frac{24}{5}=\frac{-10 + 24}{5}=\frac{14}{5}=2\frac{4}{5}$. There is an error in the options as none of them match the correct result.

Step4: Solve problem 12

When dividing $27\div(-9)$, a positive number divided by a negative number gives a negative result. $27\div(-9)=-3$. The answer is C.

Step5: Solve problem 13

To convert $5\frac{1}{3}$ to an improper fraction, use the formula $a\frac{b}{c}=\frac{a\times c + b}{c}$. So $5\frac{1}{3}=\frac{5\times3+1}{3}=\frac{16}{3}$. The answer is D.

Step6: Solve problem 14

To convert $\frac{49}{8}$ to a mixed - number, divide 49 by 8. $49\div8 = 6$ with a remainder of 1. So $\frac{49}{8}=6\frac{1}{8}$. The answer is B.

Answer:

1. No correct option
2. C. $-2\frac{2}{15}$
3. No correct option
4. C. $-3$
5. D. $\frac{16}{3}$
6. B. $6\frac{1}{8}$