Question: 9) x(7/9 - 1/6) = (14 - 3)/18 = 11/18
10) - 1/3 - (2/5 + 2) - 1/4 =
11) (-2/5 - 3) - [ -4/3 + (1 - 1/2) ] =
12) -2 - [ -1/6 - (2 + 2/3) ](-1/2) =
13) + 4/7 - { -1/3 + [ -1/4 + (2 - 1/2 + 1/3) ] - 1 } =
1. **Problem statement:** Simplify the expression $$x\left(\frac{7}{9} - \frac{1}{6}\right)$$.
2. **Formula and rules:** To subtract fractions, find a common denominator.
3. **Intermediate work:**
$$\frac{7}{9} - \frac{1}{6} = \frac{14}{18} - \frac{3}{18} = \frac{11}{18}$$
4. **Result:**
$$x \times \frac{11}{18} = \frac{11x}{18}$$
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1. **Problem statement:** Simplify $$- \frac{1}{3} - \left(\frac{2}{5} + 2\right) - \frac{1}{4}$$.
2. **Rule:** When a minus precedes parentheses, change signs inside.
3. **Intermediate work:**
$$- \frac{1}{3} - \left(\frac{2}{5} + 2\right) - \frac{1}{4} = - \frac{1}{3} - \frac{2}{5} - 2 - \frac{1}{4}$$
4. Find common denominator 60:
$$- \frac{20}{60} - \frac{24}{60} - \frac{120}{60} - \frac{15}{60} = - \frac{179}{60}$$
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1. **Problem statement:** Simplify $$\left(-\frac{2}{5} - 3\right) - \left[-\frac{4}{3} + \left(1 - \frac{1}{2}\right)\right]$$.
2. **Rule:** Remove brackets changing signs when preceded by minus.
3. **Intermediate work:**
$$-\frac{2}{5} - 3 + \frac{4}{3} - 1 + \frac{1}{2}$$
4. Common denominator 30:
$$-\frac{12}{30} - \frac{90}{30} + \frac{40}{30} - \frac{30}{30} + \frac{15}{30} = -\frac{77}{30}$$
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1. **Problem statement:** Simplify $$-2 - \left[-\frac{1}{6} - \left(2 + \frac{2}{3}\right)\right] \times \left(-\frac{1}{2}\right)$$.
2. **Rule:** Remove brackets and multiply.
3. **Intermediate work:**
Inside bracket:
$$-\frac{1}{6} - 2 - \frac{2}{3} = -\frac{1}{6} - \frac{12}{6} - \frac{4}{6} = -\frac{17}{6}$$
Multiply by $$-\frac{1}{2}$$:
$$-\frac{17}{6} \times -\frac{1}{2} = \frac{17}{12}$$
Add to $$-2$$:
$$-2 + \frac{17}{12} = -\frac{24}{12} + \frac{17}{12} = -\frac{7}{12}$$
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1. **Problem statement:** Simplify $$\frac{4}{7} - \left\{ -\frac{1}{3} + \left[ -\frac{1}{4} + \left(2 - \frac{1}{2} + \frac{1}{3}\right) \right] - 1 \right\}$$.
2. **Rule:** Remove parentheses stepwise, changing signs if preceded by minus.
3. **Intermediate work:**
Innermost parentheses:
$$2 - \frac{1}{2} + \frac{1}{3} = \frac{12}{6} - \frac{3}{6} + \frac{2}{6} = \frac{11}{6}$$
Next bracket:
$$-\frac{1}{4} + \frac{11}{6} = -\frac{3}{12} + \frac{22}{12} = \frac{19}{12}$$
Next braces:
$$-\frac{1}{3} + \frac{19}{12} - 1 = -\frac{4}{12} + \frac{19}{12} - \frac{12}{12} = \frac{3}{12} = \frac{1}{4}$$
Final expression:
$$\frac{4}{7} - \frac{1}{4} = \frac{16}{28} - \frac{7}{28} = \frac{9}{28}$$
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**Final answers:**
9) $$\frac{11x}{18}$$
10) $$-\frac{179}{60}$$
11) $$-\frac{77}{30}$$
12) $$-\frac{7}{12}$$
13) $$\frac{9}{28}$$