Multiply Rational Numbers - 7th Grade Math

1. Use distribution: What is $-2\left(\frac{1}{2}+\frac{3}{2}\right)$?

   $-4$. $-2(\frac{1}{2}+\frac{3}{2}) = -2(2) = -4$.

2. What is the value of $\frac{-5}{6}\times\frac{-3}{10}$ in simplest form?

   $\frac{1}{4}$. Negative times negative = positive; simplify: $\frac{15}{60} = \frac{1}{4}$.

3. What is $(-1)(1)$?

   $-1$. Negative times positive equals negative.

4. What is the value of $(-1)(-1)$?

   $1$. Negative times negative equals positive.

5. What is the value of $(-4)(-6)$?

   $24$. Two negatives multiply to positive: $(-4)(-6) = 24$.

6. What is the value of $(-6)(-2)$?

   $12$. Same signs: $(-6)(-2) = 12$.

7. What is $\left(-\frac{3}{4}\right)\left(\frac{8}{9}\right)$?

   $-\frac{2}{3}$. $-\frac{3}{4} \times \frac{8}{9} = -\frac{24}{36} = -\frac{2}{3}$.

8. Identify the property shown: $a(b+c)=ab+ac$.

   Distributive property. Multiplication distributes over addition.

9. What is the value of $\frac{-2}{3} \times \frac{9}{4}$?

   $\frac{-3}{2}$. Multiply numerators and denominators: $\frac{-18}{12} = \frac{-3}{2}$

10. What is $(1)(-1)$?

    $-1$. Positive times negative equals negative.

11. What is the value of $0 \times (-9)$?

    $0$. Zero times any number equals zero.

12. What is the sign of a product when one factor is negative and the other is positive, such as $(-3)(+5)$?

    Negative. A positive times a negative (or vice versa) always gives a negative product.

13. State the sign of the product when multiplying two numbers with the same sign.

    Positive. Same signs always give a positive product.

14. What is the value of $(-0.6)(5)$?

    $-3$. Negative times positive gives negative: $(-0.6)(5) = -3$.

15. What is the value of $(-1)(7)$?

    $-7$. Negative one times any number gives its opposite.

16. What is the value of $\frac{-2}{3}\times\frac{9}{4}$?

    $\frac{-3}{2}$. Multiply numerators and denominators: $\frac{-2 \times 9}{3 \times 4} = \frac{-18}{12} = \frac{-3}{2}$.

17. What is the value of $(1)(-9)$?

    $-9$. Positive times negative gives negative.

18. What does $(-2)(-6)=12$ represent if $-2$ means $2$ units below $0$ and $-6$ means reversing direction $6$ times?

    Reversing a negative gives a positive result: $12$ units above $0$. Reversing a negative direction results in positive movement.

19. What is the sign of a product when both factors are positive, such as $(+3)(+5)$?

    Positive. Two positive numbers always multiply to give a positive product.

20. Interpret the context: A bank balance changes by $(-8)$ dollars per day for $5$ days. What is the total change?

    $-40$ dollars. $(-8) \times 5 = -40$ dollars total change.

21. What is $\left(\frac{3}{5}\right)\left(-10\right)$?

    $-6$. $\frac{3}{5} \times (-10) = -\frac{30}{5} = -6$.

22. What is the value of $(0)(-15)$?

    $0$. Zero times any number equals zero.

23. Find the missing number: $(-1)(\boxed{~})=8$.

    $-8$. Since $(-1)(-8) = 8$, the missing number is $-8$.

24. What is $(-1)(0)$?

    $0$. Any number times zero equals zero.

25. What is $\left(-\frac{2}{3}\right)\left(-9\right)$?

    $6$. Negative times negative equals positive.

26. Which expression is equivalent to $-4(x-3)$?

    $-4x+12$. Distribute $-4$: $-4(x) + -4(-3) = -4x + 12$.

27. What is the value of $-3\bigl(4+(-2)\bigr)$?

    $-6$. First simplify inside: $4 + (-2) = 2$, then $-3(2) = -6$.

28. What is the value of $(-3)(4)$?

    $-12$. Different signs: $(-3)(4) = -12$.

29. State the sign of the product when multiplying two numbers with different signs.

    Negative. Different signs always give a negative product.

30. What is the value of $-2(3)+-2(5)$?

    $-16$. Distributive property: $-6 + -10 = -16$.

31. What is $(-3)(-4)$?

    $12$. Two negatives multiply to give positive.

32. What is the value of $-2(3+5)$?

    $-16$. First add inside parentheses: $-2(8) = -16$.

33. What does the product $(-3)(4)$ represent for a $4$-day change of $-3$ units per day?

    A total change of $-12$ units. Repeated addition: $4$ days of $-3$ units each.

34. What is $(-1)(-1)$?

    $1$. Negative times negative equals positive.

35. What is the value of $\frac{7}{8} \times \frac{-4}{7}$?

    $\frac{-1}{2}$. Cancel $7$s: $\frac{-4}{8} = \frac{-1}{2}$

36. Use distribution: What is $-3(2-5)$?

    $9$. $-3(2-5) = -3(-3) = 9$.

37. What is the sign of a product when both factors are negative, such as $(-3)(-5)$?

    Positive. Two negatives multiply to give a positive (negative × negative = positive).

38. What is the value of $(1)(-7)$?

    $-7$. Positive times negative gives negative result.

39. What is $\left(-\frac{2}{3}\right)\left(9\right)$?

    $-6$. $-\frac{2}{3} \times 9 = -\frac{18}{3} = -6$.

40. What is the value of $(-4)(6)$?

    $-24$. Negative times positive gives negative: $(-4)(6) = -24$.

41. Interpret the context: A diver moves $-3$ meters each second for $4$ seconds. What is the total vertical change?

    $-12$ meters. $(-3) \times 4 = -12$ meters total descent.

42. What is the value of $(-3)\big( \frac{1}{2} \big)$?

    $\frac{-3}{2}$. Negative times positive fraction gives negative.

43. What is the value of $-3(4+2)$?

    $-18$. Distribute $-3$: $-3(4) + -3(2) = -12 + -6 = -18$.

44. What is the value of $(0.6)(-5)$?

    $-3$. Positive times negative: $0.6 \times -5 = -3$.

45. What is the value of $\frac{-5}{6}\times\frac{-3}{10}$?

    $\frac{1}{4}$. Two negatives: $\frac{15}{60} = \frac{1}{4}$.

46. Which property is shown by $ab=ba$ and still holds for rational numbers?

    Commutative property of multiplication. Order doesn't matter when multiplying: $ab = ba$.

47. What is $0\cdot\left(-\frac{5}{7}\right)$?

    $0$. Zero times any number equals zero.

48. What is the sign of the product when multiplying two negative rational numbers?

    Positive. Two negatives multiply to give a positive result.

49. What property justifies rewriting $a(b+c)$ as $ab+ac$ for rational numbers?

    Distributive property. Allows multiplying each term inside parentheses separately.

50. Which property is shown by $(ab)c=a(bc)$ and still holds for rational numbers?

    Associative property of multiplication. Grouping doesn't matter when multiplying: $(ab)c = a(bc)$.

51. What does $(-3)(5)$ represent if $-3$ means "a loss of $3" and $5$ is the number of days?

    A total loss of $15. Negative (loss) times positive (days) = total negative (total loss).

52. What property is shown by $a(b+c)=ab+ac$ and is used to extend multiplication to signed numbers?

    Distributive property. Allows multiplication over addition: $a(b+c) = ab + ac$.

53. What is $-\left(\frac{2}{7}\right)\cdot\left(-14\right)$?

    $4$. $-\frac{2}{7} \times (-14) = \frac{28}{7} = 4$.

54. What is the sign of the product when multiplying a positive and a negative rational number?

    Negative. Different signs multiply to give a negative product.

55. What is $\left(-\frac{5}{6}\right)\left(-\frac{3}{10}\right)$?

    $\frac{1}{4}$. $-\frac{5}{6} \times -\frac{3}{10} = \frac{15}{60} = \frac{1}{4}$.

56. What is the value of $(-2.5)(-4)$?

    $10$. Two negatives make positive: $2.5 \times 4 = 10$.

57. What is $(-3)(4)$?

    $-12$. Negative times positive gives negative product.

Study these flashcards