Rational numbers part 2

1. Write in standard form:

(a) $12/(-240)$:

$$\frac{12}{-240} = -\frac{12}{240} = -\frac{1}{20}$$

(b) $(-19)/362$:

$$\frac{-19}{362} = -\frac{19}{362}$$

2. Using appropriate property find $-2/3×3/5+5/2×4/7+3/5×1/6$:

$$-\frac{2}{3}×\frac{3}{5}+\frac{5}{2}×\frac{4}{7}+\frac{3}{5}×\frac{1}{6} = -\frac{2}{5} + \frac{10}{7} + \frac{1}{10} = -\frac{14}{70} + \frac{100}{70} + \frac{7}{70} = \frac{93}{70} = \frac{186}{140}$$

3. What should be subtracted from the product of $3/7$ and $2/5$ to get $4/35$?

$$\frac{3}{7} × \frac{2}{5} - \frac{4}{35} = \frac{6}{35} - \frac{4}{35} = \frac{2}{35}$$

4. One sixth of the students of a class joined the sports club. Three fifth of these students opted to play table tennis. If 6 students play table tennis, how many students are there in the class?

$$\frac{1}{6} \times \frac{3}{5} = \frac{1}{10}$$ So 10 students are in the class.

5. Simplify $(10/21×(-7)/5)-(2/3×9/(-16))+((-4)/15×(-6)/16)$:

$$\frac{10}{21}×\frac{-7}{5}-\frac{2}{3}×\frac{9}{-16}+\frac{-4}{15}×\frac{-6}{16} = -\frac{14}{21} + \frac{3}{8} + \frac{1}{10} = -\frac{2}{3} + \frac{3}{8} + \frac{1}{10} = -\frac{40}{120} + \frac{45}{120} + \frac{12}{120} = \frac{17}{120}$$

6. Is $4/11$ the multiplicative inverse of $-3\ 3/4$? Give reasons.

$$\frac{4}{11} × -\frac{15}{4} = -\frac{60}{44} = -\frac{15}{11}$$ Since this result is not equal to 1, $4/11$ is not the multiplicative inverse of $-3\ 3/4$.