The document presents a prayer followed by mathematics exercises focusing on operations with integers, including addition, subtraction, multiplication, and division. It outlines rules for performing these operations and provides practice problems with solutions. Additionally, it explains the concept of integers as whole numbers, both positive and negative, including zero.

1. PRAYER
Heavenly and all POWERful Father,
we thank You for the MULTIPLE blessings
that You have given to us. Thank you for
ADDED love and INFINITE protection.
Thank you for giving us this chance to go
on with our studies. Thank You for
DIVIDING Your blessings and
DIMINISHING our sins. Always protect us
in everything that we do. In our Lord
Jesus' name, we pray, Amen

2. Sarah has 145 marbles, and her friend
gives her 230 more. How many marbles
does Sarah have now?
DRILL
DRILL
Answer:
Answer:
Answer: 145 + 230 =375

3. There were 1200 students in a school
last year, but 234 students graduated.
How many students are there now?
DRILL
DRILL
Answer:
Answer:
1200 − 234 = 966

4. Problem: A box contains 24 packs of
cookies, and each pack has 15 cookies.
How many cookies are there in total?
DRILL
DRILL
Answer:
Answer:
24 × 15 = 360

5. Problem: A total of 816 candies are to
be distributed equally among 24
children. How many candies will each
child receive?
DRILL
DRILL
Answer:
Answer:
816 ÷ 24 = 34

6. Pedro can boil an egg in exactly
Pedro can boil an egg in exactly
15 minutes. How long will it take
15 minutes. How long will it take
him to boil 10 eggs?
him to boil 10 eggs?
DRILL
DRILL
Answer:
Answer:
15 minutes
15 minutes

7. INTEGERS
INTEGERS

8. What is an
Integer?

9. • An integer is a positive or
negative whole number,
including 0.
…-3, -2, -1, 0, 1, 2, 3…

10. There are
“4”
Integer
Operations

15. 4 Integer Operations
• Addition +
• Subtraction -
• Multiplication x
• Division ÷

16. Rule #1 for
Adding Integers (+)
• The sum of two positive integers is
always positive.
5 + 1 = 6

17. Rule #2 for
Adding Integers (+)
• The sum of two negative integers is
always negative.
-5 + (-1) = -6

18. Rule #3 for
Adding Integers (+)
• The sum of a positive and a negative
integer could be positive, negative, or
zero.

19. Rule #3 for
Adding Integers Continued
• When you add a positive and negative
integer, you are really subtracting. Then,
you give the answer the sign of the
greater absolute value.
5 + (-1) = -4
-5 + 1 = 4
-5 + (-5) = 0

20. Let’s Practice “Addition”
1) 5 + 6 =
2) -3 + (-2) =
3) -6 + 5 =
4) 8 + (-7) =
5) -9 + 9 =

21.  Let’s Check
1) 5 + 6 = 11
2) -3 + (-2) = -5
3) -6 + 5 = -1
4) 8 + (-7) = 1
5) -9 + 9 = 0

22. Rules for
Subtracting Integers (-)
• To subtract an integer, add its
opposite.
• You will need to correctly change all
subtraction problems into addition
problems!

23. How do you
change a
subtraction
problem into an
addition problem?

24. There are three steps:
1. Keep the first integer the same.
(Same)
2. Change the subtraction sign into an
addition sign. (Change)
3. Take the opposite of the number that
immediately follows the newly placed
addition sign. (Change)

28. Examples:
5 – (-2) = 5 + 2 = 7
-5 – 2 = -5 + (-2) = -7
Think …
Same, Change, Change

29. Let’s Practice “Subtraction”
1) 5 – 2 =
2) -3 – 4 =
3) -1 – (-2) =
4) -5 – (-3) =
5) 7 – (-6) =

30.  Let’s Check
1) 5 – 2 = 5 + (-2) = 3
2) -3 – 4 = -3 + (-4) = -7
3) -1 – (-2) = -1 + 2 = 1
4) -5 – (-3) = -5 + 3 = -2
5) 7 – (-6) = 7+ 6 = 13

31. Rules for
Multiplying Integers (x)
• The product of two integers with the
same signs is POSITIVE.
• The product of two integers with
different signs is NEGATIVE.

32. Rules Summary for
Multiplication
• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative= Negative
• Negative x Positive = Negative

33. Let’s Practice “Multiplication”
1) 6 x (-3) =
2) 3 x 3 =
3) -4 x 5 =
4) -6 x (-2) =
5) -7 x (-8) =

34.  Let’s Check
1) 6 x (-3) = -18
2) 3 x 3 = 9
3) -4 x 5 = -20
4) -6 x (-2) = 12
5) -7 x (-8) = 56

35. Did you know that
the rules for
multiplication and
division are the
same?

36. Guess what….
They are!

37. The rules for division are exactly
the same as those for multiplication.
If we were to take the rules for
multiplication and change the
multiplication signs to division signs,
we would have an accurate set of
rules for division.

38. Rules for
Dividing Integers (÷)
• The quotient of two integers with
the same signs is POSITIVE.
• The quotient of two integers with
different signs is NEGATIVE.

39. Rules Summary for
Division
• Positive ÷ Positive = Positive
• Negative ÷ Negative = Positive
• Positive ÷ Negative= Negative
• Negative ÷ Positive = Negative

40. Let’s Practice “Division”
1) 18 ÷ (-2) =
2) -48 ÷ (-6) =
3) -27 ÷ 9 =
4) 64 ÷ 8 =
5) 30 ÷ (-5) =

41.  Let’s Check
1) 18 ÷ (-2) = -9
2) -48 ÷ (-6) = 8
3) -27 ÷ 9 = -3
4) 64 ÷ 8 = 8
5) 30 ÷ (-5) = -6

42. Let’s Review…

43. What is an integer?

44. ANSWER
• An integer is a positive or
negative whole number,
including 0.

45. Can you give an example
of an integer?

46. ANSWER
• …-3, -2, -1, 0, 1, 2, 3…

47. What are the four
operations?

48. ANSWER
• The four operations are:
addition, subtraction,
multiplication, and division.

49. How do you add
integers?

50. ANSWER
• The sum of two positive integers is always
positive.
• The sum of two negative integers is always
negative.
• When you add a positive and negative
integer, you are really subtracting. Then, you
give the answer the sign of the greater
absolute value.

51. How do you
subtract integers?

52. ANSWER
• To subtract an integer, add its
opposite.
• Same, Change, Change

53. How do you multiply
integers?

54. ANSWER
• If the signs are the same, your answer
is always positive.
• If the signs are different, your answer
is always negative.

55. How do you divide
integers?

56. ANSWER
• If the signs are the same, your answer is
always positive.
• If the signs are different, your answer is
always negative.
*Multiplication and Division Rules are the
same!