Compute Expressions 2Ec6C9

1. **Problem statement:** Compute the value of the expression $(-8)(-6)$. 2. **Formula and rules:** Multiplying two negative numbers results in a positive number. 3. **Calculation:** $$(-8)(-6) = +8 \times 6 = 48$$ 4. **Explanation:** Since both factors are negative, their product is positive. 1. **Problem statement:** Compute the value of the expression $(+4)(-9)$. 2. **Formula and rules:** Multiplying a positive number by a negative number results in a negative number. 3. **Calculation:** $$(+4)(-9) = -(4 \times 9) = -36$$ 4. **Explanation:** One factor is positive and the other is negative, so the product is negative. 1. **Problem statement:** Compute the value of the expression $(+5)(+2)(-7) + 5$. 2. **Formula and rules:** Multiply the three numbers first, then add 5. 3. **Calculation:** $$(+5)(+2)(-7) = 5 \times 2 \times (-7) = 10 \times (-7) = -70$$ $$-70 + 5 = -65$$ 4. **Explanation:** Multiplying two positives and one negative gives a negative product, then add 5. 1. **Problem statement:** Compute the value of the expression $(-9)(+10)(-7)$. 2. **Formula and rules:** Multiplying two negatives results in a positive, so multiply stepwise. 3. **Calculation:** $$(-9)(+10) = -90$$ $$-90 \times (-7) = +630$$ 4. **Explanation:** Negative times positive is negative, then negative times negative is positive. 1. **Problem statement:** Compute the value of the expression $(+72)(-8)$. 2. **Formula and rules:** Positive times negative is negative. 3. **Calculation:** $$72 \times (-8) = -576$$ 4. **Explanation:** The product is negative because one factor is negative. 1. **Problem statement:** Compute the value of the expression $(-24)(-36)$. 2. **Formula and rules:** Negative times negative is positive. 3. **Calculation:** $$(-24)(-36) = 24 \times 36 = 864$$ 4. **Explanation:** Both factors are negative, so the product is positive. 1. **Problem statement:** Compute the value of the expression $(-72) \div 6$. 2. **Formula and rules:** Dividing a negative number by a positive number results in a negative number. 3. **Calculation:** $$\frac{-72}{6} = -12$$ 4. **Explanation:** The quotient is negative because the dividend is negative. 1. **Problem statement:** Compute the value of the expression $(-16) \div (-88)$. 2. **Formula and rules:** Dividing a negative number by a negative number results in a positive number. 3. **Calculation:** $$\frac{-16}{-88} = \frac{\cancel{-16}}{\cancel{-88}} = \frac{16}{88} = \frac{2}{11}$$ 4. **Explanation:** Both numerator and denominator are negative, so the quotient is positive. 1. **Problem statement:** Compute the value of the expression $(-12)(+9)(-36)$. 2. **Formula and rules:** Multiply stepwise, negative times positive is negative, negative times negative is positive. 3. **Calculation:** $$(-12)(+9) = -108$$ $$-108 \times (-36) = 108 \times 36 = 3888$$ 4. **Explanation:** The product is positive because there are two negative factors. 1. **Problem statement:** Compute the value of the expression $(+20)(-75)(-2)$. 2. **Formula and rules:** Multiply stepwise, positive times negative is negative, negative times negative is positive. 3. **Calculation:** $$20 \times (-75) = -1500$$ $$-1500 \times (-2) = 3000$$ 4. **Explanation:** The product is positive because there are two negative factors. 1. **Problem statement:** Compute the value of the expression $\frac{5}{24} \times \frac{-8}{15}$. 2. **Formula and rules:** Multiply numerators and denominators, then simplify. 3. **Calculation:** $$\frac{5}{24} \times \frac{-8}{15} = \frac{5 \times (-8)}{24 \times 15} = \frac{-40}{360} = \frac{\cancel{-40}}{\cancel{360}} = \frac{-1}{9}$$ 4. **Explanation:** The product is negative because one fraction is negative. 1. **Problem statement:** Compute the value of the expression $(-21) \div \left(\frac{-14}{-36}\right) \times \left(\frac{-35}{42}\right)$. 2. **Formula and rules:** Division by a fraction is multiplication by its reciprocal. 3. **Calculation:** $$\frac{-14}{-36} = \frac{14}{36} = \frac{7}{18}$$ $$(-21) \div \frac{7}{18} = (-21) \times \frac{18}{7} = \frac{-21 \times 18}{7} = \frac{\cancel{-21} \times 18}{\cancel{7}} = -3 \times 18 = -54$$ $$-54 \times \frac{-35}{42} = \frac{-54 \times -35}{42} = \frac{54 \times 35}{42} = \frac{\cancel{54} \times 35}{\cancel{42}} = \frac{9 \times 35}{7} = 9 \times 5 = 45$$ 4. **Explanation:** Carefully simplify each step, noting sign changes and fraction simplifications. **Final answers:** 28. $48$ 29. $-36$ 30. $-65$ 31. $630$ 32. $-576$ 33. $864$ 34. $-12$ 35. $\frac{2}{11}$ 36. $3888$ 37. $3000$ 38. $-\frac{1}{9}$ 39. $45$