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Class 6 - Maths (Integers).pptx
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- 2. MATHEMATICS Mathematics is thescience of numbers and figures through logical reasoning.
- 3. The coldest continenton Earth is Antarctica where average temperature range from 5°C in summer to -80°C in winter. The highest temperature ever recorded in Antarctica was 15°C, while the lowest temperature ever recorded in Antarctica was -89.2°C.
- 4. In previous classes, wehave learnt about whole numbers, decimals and fractions, such as 0, 9, 5.8 and 𝟏 𝟑 .
- 5. Positive Numbers: Numbers thatare greater than 0 are called ‘positive numbers’. Such as 8, 9.8, 𝟓 𝟕 . 0 1 2 3 4 5 6
- 6. Negative Numbers: Numbers thatare less than 0 are called ‘negative numbers’. Such as -100, -1.1, - 𝟏 𝟖 0 -1 -2 -3 -4 -5 -6
- 7. Use of NegativeNumbers in the Real World Negative Numbers Are Used to Measure Temperature
- 8. Negative Numbers AreUsed to Measure Under Sea Level 0 10 20 30 -10 -20 -30 -40 -50
- 9. Negative Numbers AreUsed to Show Debt Let’s say your parents bought a car, but had to get a loan from the bank for Rs.50,000. How can we represent the amount of money your parents have as an integer? -Rs.50,000
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- 12. • An integeris a positive or negative whole number, including 0. …-3, -2, -1, 0, 1, 2, 3… Note: 0 is neither a positive nor a negative integers.
- 13. If you don’tsee a negative or positive sign in front of a number it is positive. Tip:
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- 16. Homework Practice Now (Page27) Q.1. and Q.2. (in copy)
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- 19. What is aninteger?
- 20. ANSWER • An integeris a positive or negative whole number, including 0. Note: 0 is neither a positive nor a negative integers.
- 21. Can you givean example of an integer?
- 22. ANSWER • …-3, -2,-1, 0, 1, 2, 3…
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- 31. Answer: 2 12 22.4 5 5
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- 35. Homework Practice Now (Page29) Q.1 and Q.2 (in copy)
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- 41. 4 Integer Operations •Addition + • Subtraction - • Multiplication x • Division ÷
- 42. Rule #1 for AddingIntegers (+) • The sum of two positive integers is always positive. 5 + 1 = 6
- 43. Rule #2 for AddingIntegers (+) • The sum of two negative integers is always negative. -5 + (-1) = -6
- 44. Rule #3 for AddingIntegers (+) • The sum of a positive and a negative integer could be positive, negative, or zero.
- 45. Rule #3 forAdding 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
- 46. Let’s Practice “Addition” 1)5 + 6 = • -3 + (-2) = • -6 + 5 = • 8 + (-7) = • -9 + 9 =
- 47. Let’s Check 1)5 + 6 = 11 • -3 + (-2) = -5 • -6 + 5 = -1 • 8 + (-7) = 1 • -9 + 9 = 0
- 48. Rules for Subtracting Integers(-) • To subtract an integer, add its opposite. • You will need to correctly change all subtraction problems into addition problems!
- 49. How do you changea subtraction problem into an addition problem?
- 50. There are threesteps: 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)
- 54. Same, Change, Change Examples: 5– (-2) = 5 + 2 = 7 -5 – 2 = -5 + (-2) = -7 Think …
- 55. Let’s Practice “Subtraction” 1)5 – 2 = 2) -3 – 4 = 3) -1 – (-2) = 4) -5 – (-3) = 5) 7 – (-6) =
- 56. 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
- 57. 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.
- 58. Rules Summary for Multiplication •Positive x Positive = Positive • Negative x Negative = Positive • Positive x Negative= Negative • Negative x Positive = Negative
- 59. Let’s Practice “Multiplication” 1)6 x (-3) = 2) 3 x 3 = 3) -4 x 5 = 4) -6 x (-2) = 5) -7 x (-8) =
- 60. 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
- 61. Did you knowthat the rules for multiplication and division are the same?
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- 63. • The rulesfor 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.
- 64. 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.
- 65. Rules Summary for Division •Positive ÷ Positive = Positive • Negative ÷ Negative = Positive • Positive ÷ Negative= Negative • Negative ÷ Positive = Negative
- 66. Let’s Practice “Division” 1)18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) =
- 67. Let’s Check 1)18 ÷ (-2) = -9 2) -48 ÷ (-6) = 8 3) -27 ÷ 9 = -3 4) 64 ÷ 8 = 8 5) 30 ÷ (-5) = -6
- 68. What are thefour operations?
- 69. ANSWER • The fouroperations are: addition, subtraction, multiplication, and division.
- 70. How do youadd integers?
- 71. ANSWER • The sumof 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.
- 72. How do you subtractintegers?
- 73. ANSWER • To subtractan integer, add its opposite. • Same, Change, Change
- 74. How do youmultiply integers?
- 75. ANSWER • If thesigns are the same, your answer is always positive. • If the signs are different, your answer is always negative.
- 76. How do youdivide integers?
- 77. ANSWER • If thesigns 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!