Number line

Number line

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Number line

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1. Number line

2. Definition: • It is a line drawn by a ruler and numbered starting with 0 and it is infinite. • Distance between numbers must be equal. • We use it to represent sets and operations.

3. Examples: • 1) represent the following Sets: • a) Finite Sets • Set of even numbers between 0 and 8

4. B) Infinite Sets : • Set of even numbers.

5. Operations on Sets: we Always start from 0. • 1) Addition: • Using the number line add: • 1+4=5

6. 2) Subtraction: • Using the number line Subtract: • 6-4=2

7. 3) Multiplication: • Use the number line to multiply: • 5 X 2= 10 This means 5 jumps each is 2 steps

8. Properties of Addition of Natural Numbers • Closure property: • If the sum of adding 2 numbers ∈ to N • Ex: 2 + 3 = 5 • 5∈ N so 5 is closure. • Commutative property: • This is for adding 2 N.N. and changing its place doesn’t affect the sum. • Ex: 2 + 5 = 7 a + b= b+a • 5 + 2 = 7 b + a= a+b • When we change places the answer doesn’t change

9. Associative property: • This is for adding more than 2 N.N. and we have to use brackets and we prefer to use the family of numbers. • Ex: 3 + 4 + 7 Family number: • ( 3 + 4 ) + 7 associative property 1+9=10, 2+8+10 • 7 + 7 = 14 3+7=10, 4+6=10 • ( a + b ) + c = a + ( b + c ) 5+5=10 • Or (3+7)+4 commutative and associative • 10+4=14 • Additive neutral element: • Is 0 • Ex: 0 + 5 = 5 • When we add Zero to any element the sum stays as it is doesn’t change.

10. Subtraction of N.N. • Subtract if possibleSub if Not possible in N • 6 – 3 = 3 b) 3 – 6 = -3 ( negative number) • They are not the save answer. • We can’t use the commutative and associative property in subtraction

11. Properties of Multiplication of Natural Numbers • Commutative property: • This is with the multiplication of 2 N.N. and changing its place doesn’t affect the product. • Ex: 2 x 5 = 10 a x b= bxa • 5 x 2 = 10 b x a= axb • When we change places the answer doesn’t change

12. Associative property: • This is for multiplying more than 2 N.N. and we have to use brackets and we prefer to use the family of numbers. • Ex: 2x3x5= Family number: • (2x3)x5 associative property 2x5 =10 • 20x5=100 • 6x5=30 4x25=100 8x125=1000 16x625=1000 • ( a x b ) x c = a x ( b x c )Or • (2x5)x3 commutative and associative property • 10x3=30

13. Multiplicative neutral element: • Is 1 • Ex: 1 x 5 = 5 • When we multiply any element by 1 this element doesn’t change. • Distributive of Multiplication (over addition) : • Example: 2x104 104=100+4 • 2x (100+4) • (2x100)+(2x4)= • 200+8=208

14. No properties in division. • Example1: • 18÷6=3 , 6÷18=0.333 • 3∈N , 0.333∉N • They are not equal so we can’t use the commutative property. • Example2: • (24÷4)÷2 , 24÷ (4÷2) • 6÷2 , 24÷2 • 3 , 12 • They are not equal so we can’t use the associative property. • Note: • 0÷5=0 ∈ to N.N • 5÷0= is not possible ∉ to N.N

15. Evaluation: 1)Use the number line to represent the following: A) 4+5= B) 7-3= C) 2 x 3= 2) Complete to get a true sentence: 213+57=57+…… ….. Property 28+(72+59)= (28+…..)+59 …...Property 0+4365=….. ……Property d) ….. Is the multiplicative identity. e) …... Is the Additive Neutral element