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MATHS6integers.pptx

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MATHS6integers.pptx

  1. 1. B.J.P.S Samiti’s M.V.HERWADKAR ENGLISH MEDIUM HIGH SCHOOL Integers Program: Semester: Course: NAME OF THE COURSE Sandhya S.Kulkarni 1
  2. 2. INTEGERS -5 -4 -3 -2 -1 0 1 2 3 4 5 6 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 2 Representation of integers on a number line The sign that is used is the placement of a minus sign attached to the number .This indicates that numbers with a negative sign are less than zero. These are called negative numbers
  3. 3. If a movement of only 1 is made to the left, we get the predecessor of a number Example: Predecessor of 0 is -1, Predecessor of +2 is +1, Predecessor of +7 is +6, Predecessor of -7 is -8 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 3 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 Predecessor
  4. 4. Successor If a movement of only 1 is made to the right, we get the Successor of a number Example: Successor of 0 is +1, Successor of +1 is +2, Successor of +6 is +7, Successor of -8 is -7 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 4 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8
  5. 5. INTEGERS Since profit and loss are opposite situations Profit is represented by ‘+’ sign, Loss can be represented by ‘–’ sign • Height 100 m below sea level is -100 m • Temperature of 25°C above 0°C is +25°C • Temperature of 15°C below 0°C is -15°C M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 5
  6. 6. INTEGERS Whole numbers and the negative numbers together, the new collection of numbers will look like 0, 1, 2, 3, 4, 5,..., –1, – 2, – 3,–4, –5, ... and this collection of numbers is known as Integers. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 6
  7. 7. INTEGERS Thus, we see that on a number line the number increases as we move to the right and decreases as we move to the left. Therefore, – 3 < – 2, – 2 < – 1, – 1 < 0, 0 < 1, 1 < 2, 2 < 3 so on. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 7
  8. 8. INTEGERS Compare the following pairs of numbers using > or <. 0 & -8, 5 & -5, 1 & 8, -1 & -15 Ans: 0 > -8, 5 > -5, 1< 8, -15 < -1 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 8
  9. 9. INTEGERS Example 1 : By looking at the number line, answer the following questions : Which integers lie between – 8 and – 2? Which is the largest integer and the smallest integer among them? Solution : Integers between – 8 and – 2 are – 7, – 6, – 5, – 4, – 3. The integer – 3 is the largest and – 7 is the smallest. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 9
  10. 10. INTEGERS • Every positive integer is larger than every negative integer. • Zero is less than every positive integer. • Zero is larger than every negative integer. • Zero is neither a negative integer nor a positive integer. • Farther a number from zero on the right, larger is its value. • Farther a number from zero on the left, smaller is its value. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 10
  11. 11. INTEGERS Example 1 : By referring the number line, answer the following questions :Which integers lie between – 8 and – 2? Which is the largest integer and the smallest integer among them? Solution : Integers between – 8 and – 2 are – 7, – 6, – 5, – 4, – 3. The integer – 3 is the largest and – 7 is the smallest. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 11
  12. 12. INTEGERS Write the temperatures of these places in the form of integers in the blank column. Select the Coolest place Place Temperature Siachin 10°C below 0°C - 10°C Shimla 2°C below 0°C - 2°C Ahmedabad 30°C above 0°C 30°C Delhi 20°C above 0°C 20°C Srinagar 5°C below 0°C - 5°C The Coolest place is Siachin M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 12
  13. 13. INTEGERS Write all the integers between the given pairs (write them in the increasing order.) (a) 0 and – 7 Ans: -7 -6 -5 -4 -3 -2 -1 0 (b) – 4 and 4 Ans: -4 -3 -2 -1 0 1 2 3 4 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 13
  14. 14. INTEGERS Draw a number line and answer the following : (a) Which number occurs if we move 4 numbers to the right of -2. Ans: 2 (b) Which number will we reach if we move 5 numbers to the left of 1. Ans: -3 (c) If we are at – 8 on the number line, in which direction should we move to reach – 13 ? Ans: Left (d) If we are at – 6 on the number line, in which direction should we move to reach – 1 ? Ans: Right M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 14
  15. 15. INTEGERS Additon of Integers Add when there are two positive integers like (+3) + (+2) = +5 [= 3 + 2]. Add when there are two negative integers, but the answer will take a minus (–) sign like (–2) + (–1) = – (2+1) = –3. Numbers such as 3 and – 3, 2 and – 2, when added to each other give the sum zero. They are called additive inverse of each other. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 15
  16. 16. INTEGERS When one positive and one negative integer are added the answer will take the sign of the bigger integer (Ignoring the signs of the numbers decide which is bigger). Example: Add the integers -8 and 5 i.e. -8 +5= -3 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 16
  17. 17. INTEGERS Example : Find the sum of (– 9) + (+ 4) + (– 6) + (+ 3) Solution : We can rearrange the numbers so that the positive integers and the negative integers are grouped together. We have (– 9) + (+ 4) + (– 6) + (+ 3) = (– 9) + (– 6) + (+ 4) + (+ 3) = (– 15) + (+ 7) = – 8 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 17
  18. 18. INTEGERS Subtraction of integers To subtract an integer from another integer it is enough to add the additive inverse of the integer that is being subtracted, to the other integer. Example: Subtract 6 from 10. 10 – 6 = 10 + (-6) = 4 where -6 is the additive inverse of 6 M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 18

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