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Integers

Integers. Integers. … , -3 , -2 , -1 , 0 , 1 , 2 , 3 , …. Negative integers. Positive integers. Zero. Understanding integers. A. An integer is a whole number that has a positive sign ( + ) or a negative sign (-) , including zero.

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Integers

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  1. Integers

  2. Integers … , -3 , -2 , -1 , 0 , 1 , 2 , 3 , … Negative integers Positive integers Zero

  3. Understanding integers A An integer is a whole number that has a positive sign (+) or a negative sign (-) , including zero.

  4. 2. A positive integer is a whole number with a positive sign or without any sign. Example +2 , +7, 8 , 12.

  5. 3. A negative integer is a whole number with a negative sign. Example -3 , -10 , -20.

  6. Example Write +79 in words. (b) Write negative one hundred and fifty in figures. Solution (a) Positive seventy - nine (b) -150

  7. Example State the integers from the list below. 2 1 3 5 4 -2 , + , 6 , -2.9 , 0 , Solution The integers are -2 , 6 and 0.

  8. Test Yourself 1. Write each of the following integers in words. (a) -17 (b) +23 (c) +48 (d) -69 (e) -205 (f) +416

  9. 2. Write each of the following integers in figures. (a) Negative forty - two (b) Positive nine (c) Positive sixty – eight (d) Negative two hundred and seventy State the integers from the list below. -9, ,6.2, 4, -78,- , -9.6 1 4 3 5

  10. nted Representing integers using a number line B Integers can be represented using a horizontal or a vertical number line

  11. Number line. Decreasing Increasing -5 -4 -3 -2 -1 0 1 2 3 4 5

  12. Negative integers Positive integers Zero -4 -3 -2 -1 0 1 2 3 4 Horizontal number line

  13. Positive integers 4 3 2 1 0 -1 -2 -3 -4 Zero Negative integers Vertical number line

  14. Example (a) Use a number line to represent the integers from -5 to 3. (b) Mark 6 , -3 , -1 and 4 on a number line.

  15. Solution A -5 -4 -3 -2 -1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5 6 B

  16. Test Yourself 1. Use a number line to represent the integers from (a) -3 to 4 (b) -20 to -15

  17. tol Comparing two integers C On a horizontal number line , an integer is always greater than the integers to its left and less than the integers to its right.

  18. Example -4 -3 -2 -1 0 1 2 3 -2 is greater than -4 but is less than 1.

  19. Example (a) Which integer is smaller , -5 or 3 ? (b) Which integer is greater , -2 or -8 ?

  20. Solution A -5 is smaller than 3. -5 -4 -3 -2 -1 0 1 2 3 -8 -7 -6 -5 -4 -3 -2 -1 0 B -2 is greater than -8.

  21. Test Yourself 1. Copy and complete each of the following with ‘is greater than’ or ‘is less than’ (a) -4 +2 (b) +8 -9 (c) -3 -7 (d) -10 -6 (e) +9 -20

  22. Arranging integers in order D 1. We can arrange integers in increasing or decreasing order using a number line.

  23. Example (a) Arrange -4 , 6 , -3 , 5 , 0 and 1 in increasing order. (b) Arrange 6 , 0 , 4 , -2 and -4 in decreasing order.

  24. Solution (a) Increasing order : -4, -3, 0, 1, 5, 6 (b) -4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6 Decreasing order : 6, 4, 0, -2, -4

  25. Test Yourself 1. Arrange each of the following sets of integers in increasing order. (a) -5, -3, 0, -1, 2, -4 (B) 8, -7, -5, 6, -9, 3 2. Arrange each of the following sets of integers in decrasing order. (a) 9, -12, -6, 3, 7, -10 (b) -11, -4, 8, -3, 5, -6

  26. 2. We can identify the largest integer and the smallest integer by arranging the given integers in order.

  27. Example Determine the largest integer and the smallest integer from the following set of numbers. 1, -2, 3, 0, -5

  28. solution The largest integer is 3 and the smallest integer is -5 -5 -4 -3 -2 -1 0 1 2 3

  29. Test Yourself Determine the largest integer and the smallest integer from each of following sets of integers. (a) -7, 5, -9, 3, 0, -2 (b) 8, -12, 13,-15, 7, 11 (c) -20, -15, -19, -7, -30 (d) 5, -15, -20, 15, 10, -5

  30. 3. If the pattern of a sequence of integers is determined, we can find the missing terms in the sequence

  31. Example Copy and complete the following sequence of integers. , -5, 0, 5, ,

  32. Solution , -5, 0, 5, , 10 -10 15 +5 +5 +5 +5 +5

  33. Test Yourself Copy and complete each of the following sequences of integers. (a) 9, 5, 1, , , (b) -12, , , 3, 8, (c) , , , -10, -4 (d) -32, , , -23, -20, (e) , , -13, -4,

  34. 2.2 Addition and Subtraction of Integers A Addition of Integers 1. Addition of Integers is a process of finding the sum of two or more integers.

  35. 2. Additionan Integers to a positive integer can be represented using a number line by a movement towards the positive direction, which means from left to right. For example, -2 + 4 = 2 +4 -2 -1 0 1 2

  36. 3. Adding an integer to a negative integer can be represented using a number line by a movement towards the negative direction, which means from right to left For example, 2 +(-4)=-2 -4 -2 -1 0 1 2

  37. 4. Integers with like signs are integers with the same sign. For example 2 and 5 -8 and -12

  38. 5. Integers with unlike signs are integers with different signs. For example -4 and 10 3 and -9

  39. 1 + Example Simplify each of the following. (a) 1 + (- 2) Solution 1 + (- 2) = -1 -3 -2 -1 0 1 2

  40. (b) -3 + 5 Solution -3 + 5 = 2 -3 -2 -1 0 1 2

  41. Example Evaluate 6 +(-4) + (-5). Solution 6 +(-4) + (-5) = -3 -3 -2 -1 0 1 2 3 4 5 6

  42. Example The initial temperature of a cold storage was -2 °C. Two hours later, the temperature dropped by 3 °C. When the cold storage was switched off, the temperature rose by 7 °C. What was the new temperature of the cold storage?

  43. Solution -2 +(-3)+7 =2 Therefore, the new temperature of the cold storage was 2 °C. -5 -4 -3 -2 -1 0 1 2

  44. Test Yourself Calculate each of the following. 1) 35 + (-18) 2) (-21) + 9 3) (-13) + 34 4) (-50) + (-28) 5) (-39) + 16

  45. 2. Simplify each of the following. 1) (-27) + (-35) + (-14) 2) (-79) + 94 + (-32) 3) 124 + (-215) + (-18) 4) (-116) + (-227) + (-59) + (-32) 5) (-358) + 256 + (-78) + 49 6) 874 + (-359) + (-291) + (-432)

  46. B Subtraction of Integers 1. Subtraction of integers is a process of finding the difference between two integers. 2. The difference between two integers is the number of steps required to move from the second integer to reach the first integer on a number line.

  47. (( • If you move to the right, you will get a positive integer. For example, -3 – (-8) = 5 +5 -8 -7 -6 -5 -4 -3

  48. If you move to the left, you will get a negative integer. For example, -8 – (-3) = -5 -5 -8 -7 -6 -5 -4 -3

  49. 3. To perform a subtraction involving three integers, always work out from left to right. Example Simplify 8- (-4) – 3. Solution 8- (-4) – 3 = 8 + 4 – 3 = 12 – 3 = 9

  50. Example In the morning, the temperature of a city was -3 °C. Its temperature then dropped by 5 °C in the afternoon. At night, its temperature dropped by another 4 °C. Find the temperature of the city at night.

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