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Integers

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Concepts of Integers are better explained.Please leave a comment.

Concepts of Integers are better explained.Please leave a comment.
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Integers Integers Presentation Transcript

  • Death ValleyDeath Valley, low-lying, desert region in south-easternCalifornia. It was given its name by one of 18 survivors of aparty of 30 attempting in 1849 to find a short cut to theCalifornia goldfields. Much of the valley is below sea level,and near Badwater at 86 m (282 ft) below sea level, is thelowest point in the western hemisphere
  • Mount McKinleyMount McKinley in Alaska, which is also calledDenali, is the tallest mountain in NorthAmerica, soaring 6,194 m (20,320 ft) abovesea level. During the summer the sun shines 18to 20 hours per day in this northern region,and Mount McKinley glows in a sunrise thattakes place between 2.00 a.m. and 2.30 a.m.
  • The highest elevation in North America is Mt.McKinley, which is 20,320 feet above sea level.The lowest elevation is Death Valley, which is282 feet below sea level. What is the distance from the top ofMt. McKinley to the bottom of Death Valley?
  • The total distance is the sum of 20,320and 282, which is 20,602 feet.
  • Above sea level is the opposite of below sea level
  • up g o inG
  • up g o inG
  • n w do g o inG
  • n w do g o inG
  • up g o in GGoing up is the opposite of going down. n w do g o in G
  • 5 unitsWhat is the distance between between the two per
  • Moving right is the 0pposite of moving to left.What is the distance between them?
  • Some more opposite Profit - Loss Deposit - WithdrawTemperature above zero - Temperature below zero Moving forward - Moving back ward
  • What is the distance the man covered?The distance the man covered is 0?
  • Integers are the set of whole numbersand their opposites.
  • 20 degrees below zero = -20a profit of 15 Rupees = +15a loss of 5 points = -58 steps forward = +8
  • 10 degrees above zero = +10a loss of 16 Rupees = -16a gain of 5 points = +5 or 58 steps backward = -8
  • The number line is a line labeled with the integers in increasingorder from left to right, that extends in both directions:
  • •The number line goes on forever in both directions. This is indicated by thearrows.•Whole numbers greater than zero are called positive integers. Thesenumbers are to the right of zero on the number line.•Whole numbers less than zero are called negative integers. Thesenumbers are to the left of zero on the number line.•The integer zero is neutral. It is neither positive nor negative.•The sign of an integer is either positive (+) or negative (-), except zero,which has no sign.•Two integers are opposites if they are each the same distance away fromzero, but on opposite sides of the number line. One will have a positivesign, the other a negative sign. In the number line above, +3 and -3 arelabeled as opposites.
  • For any two different places on the number line, the integer onthe right is greater than the integer on the left.Examples: 9 > 4, 9 is right to 4
  • For any two different places on the number line, the integer onthe right is greater than the integer on the left.Examples: 6 > -9, 6 is right to -9
  • For any two different places on the number line, the integer onthe right is greater than the integer on the left.Examples: -2 >-9, -2 is right to -9
  • For any two different places on the number line, the integer onthe right is greater than the integer on the left.Examples: 0 >-5, 0 is right to -5
  • The distance between two persons is 5 units. +2 +1 0 -1 -2 -3What is the distance between two persons?
  • -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8The distance between between two persons is 7 units.
  • The number of units a number is from zero on the number line.The absolute value of a number is always a positive number (or zero).We specify the absolute value of a number n by writing n inbetween two vertical bars: |n|. Examples: |6| = 6 |-12| = 12 |0| = 0 |1234| = 1234 |-1234| = 1234
  • 1)When adding integers of the same sign, we add their absolute values, and give the result the same sign.Examples: 2+5=7 (-7) + (-2) = -(7 + 2) = -9 (-80) + (-34) = -(80 + 34) = -114
  • Addition of the integer using the number line-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
  • 2+3=5-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Addition of the integer using the number line
  • -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Addition of the integer using the number line
  • -3 + -2 = - 5-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Addition of the integer using the number line
  • 2) When adding integers of the opposite signs, wetake their absolute values, subtract the smallerfrom the larger, and give the result the sign of theinteger with the larger absolute value.Example:8 + (-3) = ?The absolute values of 8 and -3 are 8 and 3.Subtracting the smaller from the larger gives8 - 3 = 5, and since the larger absolute value was8, we give the result the same sign as 8, so 8 + (-3) = 5.
  • 2) When adding integers of the opposite signs,we take their absolute values, subtract thesmaller from the larger, and give the result thesign of the integer with the larger absolutevalue.Example: -8 + (+3) = ?The absolute values of 8 and -3 are 8 and 3.Subtracting the smaller from the larger gives8 - 3 = 5, and since the larger absolute valuewas 8, we give the result the same sign as 8,so -8 + (+3) = -5.
  • Example:53 + (-53) = ?The absolute values of 53 and -53 are 53 and 53. Subtractingthe smaller from the larger gives 53 - 53 =0. The sign in thiscase does not matter, since 0 and -0 are the same. Note that 53and -53 are opposite integers.All opposite integers have this property that their sum isequal to zero.
  • -4+7 =3-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9Addition of the integer using the number line
  • Examples:In the following examples, we convert the subtractedinteger to its opposite, and add the two integers. 7 - 4 = 7 + (-4) = 3 12 - (-5) = 12 + (5) = 17 -8 - 7 = -8 + (-7) = -15 -22 - (-40) = -22 + (40) = 18Note that the result of subtracting two integers could be positive ornegative.
  • To multiply a pair of integers if both numbers have the samesign, their product is the product of their absolute values(their product is positive).If the numbers have opposite signs, their product is theopposite of the product of their absolute values (their product isnegative). If one or both of the integers is 0, the product is 0.Examples:4 × 3 = 12In the product below, both numbers are negative, so we take the productof their absolute values. (-4) × (-5) = |-4| × |-5| = 4 × 5 = 20
  • Examples:In the product of 12 × (-2), the first number is positive and thesecond is negative, so we take the product of their absolute values,which is |12| × |-2| = 12 × 2 = 24, and give this result a negative sign:-24, so 12 × (-2) = -24.In the product of (-7) × 6, the first number is negative andthe second is positive, so we take the product of theirabsolute values, which is |-7| × |6| = 7 × 6 = 42, and give thisresult a negative sign: -42, so (-7) × 6 = -42.
  • To divide a pair of integers if both integers have thesame sign, divide the absolute value of the first integerby the absolute value of the second integer.To divide a pair of integers if both integers havedifferent signs, divide the absolute value of the firstinteger by the absolute value of the second integer, andgive this result a negative sign.Examples:In the division below, both numbers are positive, so we just divide asusual.4 ÷ 2 = 2.In the division below, both numbers are negative, so we divide theabsolute value of the first by the absolute value of the second.(-24) ÷ (-3) = |-24| ÷ |-3| = 24 ÷ 3 = 8.
  • Examples:In the division (-100) ÷ 25, both number have different signs, so wedivide the absolute value of the first number by the absolute value ofthe second,which is |-100| ÷ |25| = 100 ÷ 25 = 4, and give this result a negative sign:-4, so (-100) ÷ 25 = -4.In the division 98 ÷ (-7), both number have different signs, so we dividethe absolute value of the first number by the absolute value of thesecond, which is|98| ÷ |-7| = 98 ÷ 7 = 14, and give this result a negative sign: -14, so98 ÷ (-7) = -14.