logging in or signing up WHOLE NUMBERS Abhinav M S, Kamaleswaram, Trivandrum zenthemaster Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 376 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: January 21, 2011 This Presentation is Public Favorites: 3 Presentation Description No description available. Comments Posting comment... By: hemang80 (11 month(s) ago) hi can i download ur presentation it is very very very nice i want it Saving..... Post Reply Close Saving..... Edit Comment Close By: lcsern (14 month(s) ago) Hello, your presentation is very useful for my class. Can I download it? Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript WHOLE NUMBERS : WHOLE NUMBERS Contents : Contents Predecessor and Successor. Natural numbers. Whole numbers. Properties whole number. Closure property. Commutative property. Associative property. Distributive property. Additive identity for whole numbers. Multiplicative identity for whole numbers. The number line. Patterns in whole number. Summary. Predecessor and Successor : Predecessor and Successor Predecessor : Predecessor means just before the number that is subtracted 1 from any natural number. e.g. Predecessor of 30 is 29 (30 -1 =29) Successor : Successor means just after the number that is added 1 to any natural number. e.g. successor of 90 is 91 (90+1) Natural numbers : Natural numbers Numbers starting from 1, 2, 3, 4….are called natural numbers. Natural numbers are also called counting numbers. The first natural number is 1. There is no last natural number. The natural number 1 has no predecessor. Every natural number has successor Whole Numbers : Whole Numbers The natural numbers along with zero form the collection of whole numbers. The first whole number is zero. There is no last whole number. The whole number 0 has no predecessor. Every whole number has successor. All natural numbers are also whole numbers. But all whole numbers are not natural numbers Properties of whole numbers : Properties of whole numbers Closure property. Commutative property. Associative property Distributive property Additive identity for whole numbers Multiplicative identity for whole numbers. Closure property : Closure property Under addition If we take any two whole numbers and add them, the result is always a whole number. It is not possible to find such whole numbers whose sum is not a whole number. We say that the sum of any whole number produces whole number. Since the collection of whole numbers is closed under addition is called closure property for addition of whole numbers e.g. 9+5=14, a whole number 5+9=14,a whole number Slide 8: Under multiplication The multiplication of two whole numbers is also found to be a whole number always. We say that the system of whole numbers is closed under multiplication. The collection of whole numbers is closed under multiplication. e.g. 8 x 3 = 24, a whole number 6 x 7 = 42, a whole number Inference : Whole numbers is closed under addition and also under multiplication. Slide 9: Under Subtraction The whole numbers are not closed under subtraction. e.g. 8 - 10 = -2, not a whole number 20 - 26 = -6, not a whole number Slide 10: Under Division The whole numbers are not closed under division. e.g. 9÷ 10 = 9/10, not a whole number 5÷ 3 = 5/3, not a whole number Division by zero Division by a number means subtracting that number repeatedly till we get zero. Division of a whole number by zero is not defined because repeated subtraction of zero from any whole number never gives zero at any stage of subtraction. e.g. 12 ÷ 0 =12/0, a whole number. 13 ÷ 0 =13/0, a whole number. Commutative property : Commutative property Of addition If we add any pair of whole numbers, then the result is the same for any order of the numbers of that pair. We say that addition is commutative for whole numbers. This property is known as commutativity for addition. e.g. 12+3 = 3+12 =15, a whole number 40+50=50+40=90, a whole number. Slide 12: Of multiplication If we multiply any pair of whole numbers then the result is the same for any order of the numbers of that pair. We say that multiplication is commutative for whole numbers. This property is known as commutativity for multiplication. e.g.12x3=3x12=36, a whole number. Additions and multiplications are commutative for whole numbers but subtractions and divisions are not commutative for whole numbers. associative property : associative property Whole numbers are associative under addition and multiplication e.g. Addition:- 8+7+6 = (8+7)+6 = 8+(7+6) = 15+6 = 8 + 13 = 21 =21 The result are same. e.g. Multiplication 6x5x4 = (6x5)x4 = 6x(5x4) = 30x4 = 6x20 = 120 =120 The result are equal. Subtraction and division are not under this property of the whole numbers. Distributive Property : Distributive Property Of multiplication over addition we have, 6x(5+7) =6x5+6x7 =30 + 42 6x12 = 72 This property is know as distributive property of multiplication over addition Additive identity for whole numbers : Additive identity for whole numbers The number zero has a special role in addition A whole number remains unchanged when it is added to zero or zero is added to that number. So zero is called the additive identity for whole numbers. e.g. 8+0=8 0+9=9 Zero has a special role in multiplication too. Any number when multiplied by zero or zero multiplied by any number, results into zero. e.g. 89x0 = 0 0x78= 0 multiplicative identity for whole numbers : multiplicative identity for whole numbers A whole number remains unchanged when it is multiplied by 1 or 1 is multiplied by that number. So one is called the multiplicative identity for whole numbers. e.g. 12x1 = 12 1x35= 35 The number line. : The number line. Draw a line. Mark a point on it. Label it zero. Mark a second point to the right of zero. Label it 1. The distance between these points labeled as 0 and 1 is called unit distance. On this line mark a point to the right of one on at unit distance from 1, label it 2. In this way go on labeling points at unit distances as 3,4,5……… on the line. We can go to any whole number on the right. This is a number line for the whole numbers Slide 18: On the number line out of any two whole numbers, the number on the right of the other number is the greater number. For example: the number 7 is on the right of 4. This number 7 is greater than 4 that is 7>4. On the number line, out of any two whole numbers, the number on the left of the other number is the smaller number. For example 4<9 is on the left of 9. On the number line, the smallest whole number will be the farthest left and the greatest whole number will be the farthest right Addition on the number line : Let us show the addition of 3 and 4 The point at the tip of the arrow is 3. Start at 3. Since we add 4 to this number so we make four jumps to the right; from 3 to 4, 4 to 5, 5 to 6, and 6 to 7 as shown above the tip of the last arrow in the fourth jump is at 7. the sum of 3 and 4 is 7 i.e. 3+4=7. Addition on the number line Subtraction on the number line : Subtraction on the number line We can show the subtraction of two whole numbers on the number line. Let us show 7 – 5 The point at the tip of the arrow is 7. Start at 7. Since 5 is being subtracted, so move towards left with one jump of one unit. Make 5 such jumps. We reach the point two. We get 7 – 5 = 2 Multiplication on the number line : Multiplication on the number line We can show the multiplication of whole numbers on the number line. Let us show 3 x 4 Starting from 0 move 3 units at a time to the right, make such four moves. We will reach 12. So we say 3x4=12 Successor and predecessor on the number line : Successor and predecessor on the number line The successor of any whole number is on the immediate right of that whole number on the number line. For example: consider the successor of 12 on the number line. It is 13 The predecessor of any whole number is on the immediate left of that whole number on the number line. For example: consider the predecessor of 7 on the number line. It is 6 Pattern in whole numbers. : Pattern in whole numbers. We shall try to arrange numbers in elementary shapes made up of dots. The shapes we take are (1)a line (2)a rectangle (3)a square and (4)a rectangle. Every number should be arranged in one of these shapes. No other shape is allowed. Every number can be arranged as a line The number two is show as • • The number three is shown as • • • and so on Some numbers can be shown also as rectangles. E.g. The number 6 can be shown as a rectangle . Note there are two rows and 3 columns. We take the number of rows to be smaller than the number of columns. Also we should have more than one row in rectangle. Slide 24: Some numbers like 4 or 9 can be arranged as square; 4 9 Note, every square number is also a rectangular number. Some numbers can also be arranged as triangles. For e.g., 3 6 Note that the triangle should have its two sides equal. The number of dots in the row starting from the bottom should be like 4, 3, 2, 1. The top row should always have one dot. summary : summary The numbers 1, 2, 3, ……….. which we use for counting are known as natural numbers. If you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor. Every natural number has a successor. Every natural number except 1 has a predecessor. If we add the number zero to the collection of natural numbers, we get the collection of whole numbers. Thus the numbers 0, 1, 2, 3, ………from the collection of whole numbers. Slide 26: Every whole number has a successor. Every whole number except zero has a predecessor. All natural numbers are whole numbers, but all whole numbers are not natural numbers. We take a line, mark a point on it and label it 0. We then mark out to the right of 0, points at equal intervals. Label them as 1, 2, 3, ……. . Thus we have a number line with 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 to the right on the number line, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance starting from zero. Slide 27: Adding two whole numbers always gives a whole number. Similarly, multiplying two whole 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 and under division. Division by zero is not defined. Zero is the identity for addition of whole numbers. The whole number 1 is the identity for multiplication of whole numbers. You can add two whole numbers in any order. You can multiply two whole numbers in any order. We say that addition and multiplication are commutative for whole numbers. Slide 28: Multiplication is distributive 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 only interesting, but are useful especially for mental calculations and help us understand properties of numbers better. PowerPoint project submitted byAbhinav M. S of standard 6 D : PowerPoint project submitted byAbhinav M. S of standard 6 D THE END You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
WHOLE NUMBERS Abhinav M S, Kamaleswaram, Trivandrum zenthemaster Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 376 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: January 21, 2011 This Presentation is Public Favorites: 3 Presentation Description No description available. Comments Posting comment... By: hemang80 (11 month(s) ago) hi can i download ur presentation it is very very very nice i want it Saving..... Post Reply Close Saving..... Edit Comment Close By: lcsern (14 month(s) ago) Hello, your presentation is very useful for my class. Can I download it? Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript WHOLE NUMBERS : WHOLE NUMBERS Contents : Contents Predecessor and Successor. Natural numbers. Whole numbers. Properties whole number. Closure property. Commutative property. Associative property. Distributive property. Additive identity for whole numbers. Multiplicative identity for whole numbers. The number line. Patterns in whole number. Summary. Predecessor and Successor : Predecessor and Successor Predecessor : Predecessor means just before the number that is subtracted 1 from any natural number. e.g. Predecessor of 30 is 29 (30 -1 =29) Successor : Successor means just after the number that is added 1 to any natural number. e.g. successor of 90 is 91 (90+1) Natural numbers : Natural numbers Numbers starting from 1, 2, 3, 4….are called natural numbers. Natural numbers are also called counting numbers. The first natural number is 1. There is no last natural number. The natural number 1 has no predecessor. Every natural number has successor Whole Numbers : Whole Numbers The natural numbers along with zero form the collection of whole numbers. The first whole number is zero. There is no last whole number. The whole number 0 has no predecessor. Every whole number has successor. All natural numbers are also whole numbers. But all whole numbers are not natural numbers Properties of whole numbers : Properties of whole numbers Closure property. Commutative property. Associative property Distributive property Additive identity for whole numbers Multiplicative identity for whole numbers. Closure property : Closure property Under addition If we take any two whole numbers and add them, the result is always a whole number. It is not possible to find such whole numbers whose sum is not a whole number. We say that the sum of any whole number produces whole number. Since the collection of whole numbers is closed under addition is called closure property for addition of whole numbers e.g. 9+5=14, a whole number 5+9=14,a whole number Slide 8: Under multiplication The multiplication of two whole numbers is also found to be a whole number always. We say that the system of whole numbers is closed under multiplication. The collection of whole numbers is closed under multiplication. e.g. 8 x 3 = 24, a whole number 6 x 7 = 42, a whole number Inference : Whole numbers is closed under addition and also under multiplication. Slide 9: Under Subtraction The whole numbers are not closed under subtraction. e.g. 8 - 10 = -2, not a whole number 20 - 26 = -6, not a whole number Slide 10: Under Division The whole numbers are not closed under division. e.g. 9÷ 10 = 9/10, not a whole number 5÷ 3 = 5/3, not a whole number Division by zero Division by a number means subtracting that number repeatedly till we get zero. Division of a whole number by zero is not defined because repeated subtraction of zero from any whole number never gives zero at any stage of subtraction. e.g. 12 ÷ 0 =12/0, a whole number. 13 ÷ 0 =13/0, a whole number. Commutative property : Commutative property Of addition If we add any pair of whole numbers, then the result is the same for any order of the numbers of that pair. We say that addition is commutative for whole numbers. This property is known as commutativity for addition. e.g. 12+3 = 3+12 =15, a whole number 40+50=50+40=90, a whole number. Slide 12: Of multiplication If we multiply any pair of whole numbers then the result is the same for any order of the numbers of that pair. We say that multiplication is commutative for whole numbers. This property is known as commutativity for multiplication. e.g.12x3=3x12=36, a whole number. Additions and multiplications are commutative for whole numbers but subtractions and divisions are not commutative for whole numbers. associative property : associative property Whole numbers are associative under addition and multiplication e.g. Addition:- 8+7+6 = (8+7)+6 = 8+(7+6) = 15+6 = 8 + 13 = 21 =21 The result are same. e.g. Multiplication 6x5x4 = (6x5)x4 = 6x(5x4) = 30x4 = 6x20 = 120 =120 The result are equal. Subtraction and division are not under this property of the whole numbers. Distributive Property : Distributive Property Of multiplication over addition we have, 6x(5+7) =6x5+6x7 =30 + 42 6x12 = 72 This property is know as distributive property of multiplication over addition Additive identity for whole numbers : Additive identity for whole numbers The number zero has a special role in addition A whole number remains unchanged when it is added to zero or zero is added to that number. So zero is called the additive identity for whole numbers. e.g. 8+0=8 0+9=9 Zero has a special role in multiplication too. Any number when multiplied by zero or zero multiplied by any number, results into zero. e.g. 89x0 = 0 0x78= 0 multiplicative identity for whole numbers : multiplicative identity for whole numbers A whole number remains unchanged when it is multiplied by 1 or 1 is multiplied by that number. So one is called the multiplicative identity for whole numbers. e.g. 12x1 = 12 1x35= 35 The number line. : The number line. Draw a line. Mark a point on it. Label it zero. Mark a second point to the right of zero. Label it 1. The distance between these points labeled as 0 and 1 is called unit distance. On this line mark a point to the right of one on at unit distance from 1, label it 2. In this way go on labeling points at unit distances as 3,4,5……… on the line. We can go to any whole number on the right. This is a number line for the whole numbers Slide 18: On the number line out of any two whole numbers, the number on the right of the other number is the greater number. For example: the number 7 is on the right of 4. This number 7 is greater than 4 that is 7>4. On the number line, out of any two whole numbers, the number on the left of the other number is the smaller number. For example 4<9 is on the left of 9. On the number line, the smallest whole number will be the farthest left and the greatest whole number will be the farthest right Addition on the number line : Let us show the addition of 3 and 4 The point at the tip of the arrow is 3. Start at 3. Since we add 4 to this number so we make four jumps to the right; from 3 to 4, 4 to 5, 5 to 6, and 6 to 7 as shown above the tip of the last arrow in the fourth jump is at 7. the sum of 3 and 4 is 7 i.e. 3+4=7. Addition on the number line Subtraction on the number line : Subtraction on the number line We can show the subtraction of two whole numbers on the number line. Let us show 7 – 5 The point at the tip of the arrow is 7. Start at 7. Since 5 is being subtracted, so move towards left with one jump of one unit. Make 5 such jumps. We reach the point two. We get 7 – 5 = 2 Multiplication on the number line : Multiplication on the number line We can show the multiplication of whole numbers on the number line. Let us show 3 x 4 Starting from 0 move 3 units at a time to the right, make such four moves. We will reach 12. So we say 3x4=12 Successor and predecessor on the number line : Successor and predecessor on the number line The successor of any whole number is on the immediate right of that whole number on the number line. For example: consider the successor of 12 on the number line. It is 13 The predecessor of any whole number is on the immediate left of that whole number on the number line. For example: consider the predecessor of 7 on the number line. It is 6 Pattern in whole numbers. : Pattern in whole numbers. We shall try to arrange numbers in elementary shapes made up of dots. The shapes we take are (1)a line (2)a rectangle (3)a square and (4)a rectangle. Every number should be arranged in one of these shapes. No other shape is allowed. Every number can be arranged as a line The number two is show as • • The number three is shown as • • • and so on Some numbers can be shown also as rectangles. E.g. The number 6 can be shown as a rectangle . Note there are two rows and 3 columns. We take the number of rows to be smaller than the number of columns. Also we should have more than one row in rectangle. Slide 24: Some numbers like 4 or 9 can be arranged as square; 4 9 Note, every square number is also a rectangular number. Some numbers can also be arranged as triangles. For e.g., 3 6 Note that the triangle should have its two sides equal. The number of dots in the row starting from the bottom should be like 4, 3, 2, 1. The top row should always have one dot. summary : summary The numbers 1, 2, 3, ……….. which we use for counting are known as natural numbers. If you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor. Every natural number has a successor. Every natural number except 1 has a predecessor. If we add the number zero to the collection of natural numbers, we get the collection of whole numbers. Thus the numbers 0, 1, 2, 3, ………from the collection of whole numbers. Slide 26: Every whole number has a successor. Every whole number except zero has a predecessor. All natural numbers are whole numbers, but all whole numbers are not natural numbers. We take a line, mark a point on it and label it 0. We then mark out to the right of 0, points at equal intervals. Label them as 1, 2, 3, ……. . Thus we have a number line with 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 to the right on the number line, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance starting from zero. Slide 27: Adding two whole numbers always gives a whole number. Similarly, multiplying two whole 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 and under division. Division by zero is not defined. Zero is the identity for addition of whole numbers. The whole number 1 is the identity for multiplication of whole numbers. You can add two whole numbers in any order. You can multiply two whole numbers in any order. We say that addition and multiplication are commutative for whole numbers. Slide 28: Multiplication is distributive 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 only interesting, but are useful especially for mental calculations and help us understand properties of numbers better. PowerPoint project submitted byAbhinav M. S of standard 6 D : PowerPoint project submitted byAbhinav M. S of standard 6 D THE END