Mathematics Chapter 3 and 4
Terms
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Different ways of looking at things you can do
- Vedic
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32+32+32+32+32=160
(Multiplication)
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Repeated addition
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23 base 4 x 12 base 4=
3 x 2 = 6--> 1 2
2 x 2 = 4--> 1 0
1 x 3 = 3--> 0 3
2 x 1 = 2--> 0 2
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Traditional Multiplication in different bases
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74 + 83 = 157
70 + 80 =150
4 + 3 = 7
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Adding from the left
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87 + 32 = 119
87 + 30 = 117
Subtracted 2 to get to 30 so add on 2 more to the previous answer
- Breaking and Bridging
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Grouping numbers to make things easier
2 + 5 + 8 + 5 + 3 = 23
2 + 8 = 10
5 + 5 = 10
3
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Compatible numbers
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80 - 59 = 21
59 + 1 = 60
60 + ? = 80
60 + 20 = 80
20 + 1 = 21
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Cashier (work backwards)
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A guess which means there is no right or wrong answer
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Estimation
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-2 -1 0 1 2
<--------------->
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Number line model
- When creating a charged field you add in +- inorder to add in some.
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Charge field
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5 - 3 = 2
5 - 2 = 3
5 - 1 = 4
5 - 0 = ?
5
- Patterens
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All even numbers are divisible by 2
2, 4, 6, 8
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Divisible by 2
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Sum of all the digits are divisible by 3
561 = 5 + 6 + 1-->12
12 is divisible by 3
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Divisible by 3
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Last two digits have to be divisible by for
824 = 24 is divisible by four
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Divisible by 4
- If a number ends in 5 or 0
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Divisible by 5
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Divisible by 2 and 3
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Divisible by 6
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The last 3 digits are divisible by 8
888 is divisible by 8
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Divisible by 8
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The sum is divisible by 9
54 = 5 + 4 = 9
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Divisible by 9
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Ends in 0 in the ones place
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Divisible by 10
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4 = 4, 8 , 12, 16, 20, 24, 28
5 = 5, 10, 15, 20, 25
20 and 20
- Intersection of sets (elementary level)
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18 = 6 and 3 = 2 3 and 3
12 = 2 2 3
List what is in common once-->2 x 3 = 6
List what is left-->3 x 2 = 6
Multiply both = 6 x 6 = 36
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Least Common Multiple Prime factorization
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72 and 192
72 = 9 and 8--> 3 3 and 2 2 2
192 = 8 and 24--> 2 2 2 and 6 and 4--> 2 2 2 and 2 3 and 2 2
List everything in common 3 2 2 2 = 24
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Greatest Common Divisor Prime Factorization