1. The document discusses rules for multiplying integers, including: multiplying two numbers with the same sign results in a positive product, and multiplying two numbers with different signs results in a negative product. 2. Examples are provided to illustrate multiplying integers and checking the sign of the product based on the signs of the factors. 3. An additional rule is introduced - if the number of negative factors in a product is odd, the product is negative, and if it is even, the product is positive.

3. 1. multiply integers
2. be observant of the signs when
multiplying integers

5. follows the same
algorithm when
the only difference is when
you’re dealing with .

6. 4 × 3 = 12
We normally use this multiplication symbol to imply
multiplication.

7. 4 3 =× 12
But in algebra we don’t use multiplication symbol
anymore instead we use a to imply multiplication.

8. 4 3 12
But then again, the dot is seldom used in manipulating
algebraic or polynomial expressions. Instead, we most of
the time use on implying multiplication.
( =)

9. follows the same
algorithm when
the only difference is when
you’re dealing with .

10. Rules in Multiplying Integers
1. When you multiply two numbers with the , the
product is .
+ + = (+) − − = +
2. When you multiply two numbers with , the
product is .
+ − = (−) − + = (−)
3. Any multiplied by 0 gives a product of .

11. Example 1:
5 (−7) 35
1. Multiply. 2. Check the sign.
Multiply.
=

12. Example 1:
5 (−7) 35
1. Multiply. 2. Check the sign.
Check the sign.
=
UNLIKE signs.
+

13. Example 1:
5 (−7) 35
1. Multiply. 2. Check the sign.
Check the sign.
= −
UNLIKE signs.

14. Example 1:
5 (−7) 35
1. Multiply. 2. Check the sign.
= −

15. Example 2:
3 (−9) 27
1. Multiply. 2. Check the sign.
Multiply.
=

16. Example 2:
3 (−9) 27
1. Multiply. 2. Check the sign.
Check the sign.
=
UNLIKE signs.
+

17. Example 2:
3 (−9) 27
1. Multiply. 2. Check the sign.
Check the sign.
= −
UNLIKE signs.

18. Example 2:
3 (−9) 27
1. Multiply. 2. Check the sign.
= −

19. Example 3:
(−5)(2) 10
1. Multiply. 2. Check the sign.
Multiply.
=

20. Example 3:
(−5)(2) 10
1. Multiply. 2. Check the sign.
=
Check the sign.
UNLIKE signs.
−

21. Example 3:
(−5)(2) 10
1. Multiply. 2. Check the sign.
= −

22. Example 4:
(−9)(7) 63
1. Multiply. 2. Check the sign.
Multiply.
=

23. Example 4:
(−9)(7) 63
1. Multiply. 2. Check the sign.
=
Check the sign.
UNLIKE signs.
−

24. Example 4:
(−9)(7) 63
1. Multiply. 2. Check the sign.
= −

25. Example 4:
3 (6) 18
1. Multiply. 2. Check the sign.
Multiply.
=

26. Example 4:
3 (6) 18
1. Multiply. 2. Check the sign.
=
Check the sign.
LIKE signs.
+

27. Example 4:
3 (6) 18
1. Multiply. 2. Check the sign.
=

28. Example 5:
7 (7) 49
1. Multiply. 2. Check the sign.
Multiply.
=

29. Example 5:
7 (7) 49
1. Multiply. 2. Check the sign.
=
Check the sign.
LIKE signs.
+

30. Example 5:
7 (7) 49
1. Multiply. 2. Check the sign.
=

31. Example 6:
−2 (−3) 6
1. Multiply. 2. Check the sign.
Multiply.
=

32. Example 6:
−2 (−3) 6
1. Multiply. 2. Check the sign.
=
Check the sign.
LIKE signs.

33. Example 6:
−2 (−3) 6
1. Multiply. 2. Check the sign.
=

34. Multiply.Zero factor.
Example 7:
−192 (0) 0
1. Multiply. 2. Check the sign.
=

35. Got
questions?

37. Multiply the following integers.
1. 9(2)
2. −2(−5)
3. 8(−5)
4. −4(−9)
5. −8(1)
6. (−5)(−6)
7. −7(−8)
8. 0(−4)
9. −1(−49)
10.(2)(−2)
= 18
= 10
= −40
= 36
= −8
= 30
= 56
= 0
= 49
= −4
1. Multiply. 2. Check the sign.

38. Got
questions?

40. Rule for a Product with No Zero Factors
1. If the number of negative factors is , the
product is .
2. If the number of negative factors is , the
product is .

41. Multiply.
Example 1:
−2 −3 (5) 30=
2 36(5)
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

42. Count the number of
.
Example 1:
−2 −3 (5) 30=
Two so it is that means the sign of the
product is .
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

43. Example 1:
−2 −3 (5) 30=
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

44. Multiply.
Example 2:
−6 −2 (−5)(−8) 480=
6 212 (5)60 (8)
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

45. Example 2:
−6 −2 (−5)(−8) 480=
Count the number of
.
Four so it is that means the sign of the
product is .
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

46. Example 2:
−6 −2 (−5)(−8) 480=
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

47. Multiply.
Example 3:
−1 −2 (−3)(−4)(−5) 120=
1 22 (3)6 (4)24 (5)
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

48. Example 3:
−1 −2 (−3)(−4)(−5) 120=
Count the number of
.
Five so it is that means the sign of the
product is .
−
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

49. Example 3:
−1 −2 (−3)(−4)(−5) 120= −
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.

50. Got
questions?

52. Multiply the following integers.
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.
1. −2 2 (−2)(−2)
2. −52 62 (−13)(0)(10)(−22)
3. −3 −1 (−1)(−6)
2. −2 1 (−10)(−1)(−1)(5)
3. [ −2 3 ](−4)(10)

53. Answers!

54. Multiply the following integers.
Rule for a Product with No Zero Factors
1. If the number of negative factors is , the product is .
2. If the number of negative factors is , the product is .
1. Multiply
2. Check the sign.
1. −2 2 (−2)(−2)
2. −52 62 (−13)(0)(10)(−22)
= −16
= 0
3. −3 −1 (−1)(−6) = 18
2. −2 1 (−10)(−1)(−1)(5) = 100
3. [ −2 3 ](−4)(10) = 240

55. Got
questions?

56. E-Math 7
Practice and Application
Test I
Test III
Page 44