{"id":10901,"date":"2026-11-02T02:04:39","date_gmt":"2026-11-02T02:04:39","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10901"},"modified":"2026-11-02T02:04:39","modified_gmt":"2026-11-02T02:04:39","slug":"whole-numbers","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/whole-numbers\/","title":{"rendered":"Whole Numbers"},"content":{"rendered":"
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KAPDEC® | Elite STEM Learning Platform | https:\/\/kapdec.com<\/a><\/p>\n

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Unit<\/strong>: Number System<\/h2>\n

Chapter<\/strong>: Whole Numbers<\/h3>\n

Reference:<\/strong> \u2013 Introduction to Whole Numbers, Natural Numbers vs Whole Numbers, The Number Line, Successor and Predecessor, Properties of Whole Numbers (Closure, Commutativity, Associativity, Distributivity, Identity), Addition & Subtraction on the Number Line, Multiplication & Division, Patterns in Whole Numbers<\/em><\/p>\n

After studying this chapter, you should be able to understand:<\/p>\n

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  • Introduction to Whole Numbers & Their Need<\/li>\n
  • Natural Numbers vs Whole Numbers<\/li>\n
  • Representing Whole Numbers on the Number Line<\/li>\n
  • Successor and Predecessor<\/li>\n
  • Properties of Whole Numbers (Closure, Commutative, Associative, Distributive, Identity)<\/li>\n
  • Operations on Whole Numbers & Their Properties<\/li>\n
  • Patterns in Whole Numbers<\/li>\n<\/ul>\n

    \nWhole Numbers<\/strong><\/p>\n

    \u00a0<\/p>\n

    We use 1, 2, 3, 4,… when we begin to count. They come naturally when we start counting. Hence, mathematicians call the counting numbers as Natural numbers<\/strong>.<\/p>\n

    \u00a0<\/p>\n

      \n
    • To find the next counting number, we add 1 to the counting number. This new number is also called the successor of the counting number.<\/li>\n
    • To find the previous counting number, we subtract 1 from the counting number. This new number is also called the predecessor of the counting number.<\/li>\n
    • The number 4 has 3 as its predecessor and 5 as its successor. Similarly, the successor of 2 is 3 and the predecessor is 1.<\/li>\n<\/ul>\n

      \u00a0<\/p>\n

      But is there any natural number which has no successor? Is there a last natural number?<\/strong><\/p>\n

      \u00a0<\/p>\n

      There exist countable things like number of students in a class or number of red buses on road. There also exists things like number of sugar granules in 1 kg of sugar or number of stars in the sky which cannot be counted. Even if they were countable, a number would exist to state their count. We can always get a new number by adding 1 to it. So, we can say there does not exist any last natural number.<\/p>\n

      \u00a0<\/p>\n

      Does 1 have both a successor and a predecessor?<\/strong><\/p>\n

      The successor of 1 is 2. But the number 1 has no predecessor in natural numbers. We add zero as the predecessor for 1 to the collection of natural numbers.<\/p>\n

      BUT – The natural numbers along with zero form the collection of whole numbers.<\/strong><\/p>\n

      1. Are all the natural numbers also whole numbers?<\/p>\n

      2. Are all whole numbers also natural numbers?<\/p>\n

      3. Which is the greatest whole number?<\/p>\n

      \u00a0<\/p>\n

      The Number Line<\/strong><\/p>\n

      We have seen the number line for natural numbers start from 1.<\/p>\n

      When we mark a point 0, towards the left of point 1, this becomes a number line for whole numbers.<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      Addition on the Number Line-<\/strong><\/p>\n

      Addition of whole numbers can be shown on the number line.<\/p>\n

      Let us see the addition of 2 and 5.<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      We start from zero. For 2, we make move 2 units towards right. Since we add 5 to this number so we move5units further to the right.<\/p>\n

      The sum of 2 and 5 is 7, i.e. 2 + 5 = 7.<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

      Subtraction on the Number Line:<\/strong><\/p>\n

      The subtraction of two whole numbers can also be shown on the number line.<\/p>\n

      Let us find 7 \u2013 5.<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0<\/p>\n

      We start from zero. For 7, we make move 7 units towards right. Since we subtract5from this number so we move5units to the left from point 7.<\/p>\n

      The difference of 7 and 5 is 2, i.e. 7-5 = 2.<\/p>\n

      \u00a0<\/p>\n

      \u00a0<\/p>\n

      Multiplication on the Number Line-<\/strong><\/p>\n

      We now see the multiplication of whole numbers on the number line.<\/p>\n

      Let us find 2 \u00d7 4<\/p>\n

      \"\"<\/p>\n

      Source: Kapdec.com<\/p>\n<\/div>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

      Multiplying 2 by 4 is same as adding 2 four times. To multiply, we start from zero and make 4 jumps of 2 units each towards right.<\/p>\n

      The product of 2 and 4 is 8, i.e. 2 \u00d7 4 = 8.<\/p>\n

      \u00a0<\/p>\n

      Magic or Maths??<\/u><\/strong><\/p>\n

      1089 trick<\/strong><\/p>\n

      \u00a0<\/p>\n

      Step #1:<\/strong> Write down any three digits number with\u00a0decreasing digits.<\/p>\n

      \nStep #2:<\/strong> Reverse the number you wrote in step #1.\u00a0<\/p>\n

      \u00a0<\/p>\n

      Step #3:<\/strong> Subtract the number obtained in step #2 from the number you wrote in step #1<\/p>\n

      \u00a0<\/p>\n

      Step #4:<\/strong> Reverse the number obtained in step #3<\/p>\n

      \u00a0<\/p>\n

      Step #5:<\/strong> Add the numbers found in step #3 and step #4<\/p>\n

      You will find that the result is always 1089<\/strong><\/p>\n

      \u00a0<\/p>\n

      <\/p>\n