## Pre-Requisires

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**Whole Numbers | Speed Notes**

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**Whole Numbers** The numbers 1,2, 3, ……which we usefor counting areknown as natural numbers. If you add1 to a natural number, we get itssuccessor. If yousubtract 1 froma natural number, you get itspredecessor. (Scroll down to continue …)

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Every natural number has a successor. Every natural number except 1 has apredecessor. If we addthe number zeroto the collection of natural numbers, we get thecollection of whole numbers. Thus, the numbers 0, 1, 2, 3, … form the collection of whole numbers. Every wholenumber has asuccessor. Every whole number except zerohas a predecessor. All natural numbers are wholenumbers, but allwhole numbers arenot natural numbers. We take a line, mark a point on it and label it 0. We then mark out points to the right of 0, at equal intervals. Label them as1, 2, 3,…………………………………. Thus, we havea number linewith the whole numbers represented on it.We can easily perform the number operations of addition, subtraction and multiplication on the number line. Addition corresponds to moving tothe right onthe number line, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance starting from zero. Addingtwo whole numbers always gives a whole number. Similarly, multiplying twowhole numbers always gives a whole number. We say that whole numbers are closed under addition and also under multiplication. However, whole numbers are not closed under subtraction andunder division. Division by zerois not defined. Zero is theidentity for addition of whole numbers. The whole number 1 is theidentity for multiplication of whole numbers. You can addtwo whole numbers in any order. You can multiply two whole numbers in anyorder. We saythat addition andmultiplication are commutative for whole numbers. Addition and multiplication, both, are associative for whole numbers. Multiplication isdistributive over addition for whole numbers. Commutativity, associativity and distributivity properties of whole numbers are useful in simplifying calculations and we use them without being aware of them.Patterns with numbers are not onlyinteresting, but areuseful especially forverbal calculations and helpus to understand properties of numbers better.

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