vb.net qr code generator Introduction to Variables in Visual Studio .NET

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CHAPTER 2 Introduction to Variables
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2 x 2 x 2 1: x x x x Simply because a plus or minus sign appears in a fraction does not auto3 x matically mean that canceling is not appropriate For instance 1 3 x because any nonzero quantity divided by itself is one
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2 3x x 1 2 3x x 1 x 1: 2 3x 2 3x 1 The reason 2 + 3x can be canceled is that 2 + 3x is a factor of (2 + 3x)(x 1) 2 x 7 3x 1 2 x 7 3x 1 x 7 3x 1 2 2 1 15 x 6 x 2 3 5 x 6 x 2 3 x 2 5 x 6 5 x 6 3 x 2 3 x 2 3 x 2 1
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1: 2: 3: 4: 5: 6: 3xy 2x 8x 4 30xy 16y 72x 18xy x x 6 2x 6xy 2x 1 3x
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CHAPTER 2 Introduction to Variables
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5x 16 2x 7 6 2x 7 24x y 8 x 1 15x y 8 150xy 2x 17 8x 3 48y
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1: 2: 3: 4: 5: 6: 7: 8: 9: 3xy 3y x 3y 2x 2 x 2 8x 2x 4 2x 4 1 4 30xy 15x 2y 15x 16y 8 2y 8 72x 4 18x 4 18xy y 18x y x x 6 x 6 x x 6 2x 2 x 2 6xy 2x 1 2y 2x 1 3x 2y 2x 1 3x 1 3x 5x 16 2x 7 5x 16 2x 7 5x 16 6 2x 7 6 2x 7 6 24x y 8 x 1 8 x 1 3x y 8 8 x 1 15x y 8 5 3x y 8 5 150xy 2x 17 8x 3 25x 2x 17 8x 3 6y 48y 8 6y 25x 2x 17 8x 3 8
CHAPTER 2 Introduction to Variables
Operations on Fractions with Variables
Multiplication of fractions with variables is done in exactly the same way as multiplication of fractions without variables multiply the numerators and multiply the denominators
Examples
7 3x 21x 10 4 40 24 3 24 3 12 3 36 5y 14 5y 14 5y 7 35y 34x 3 34x 3 17x 1 17x 15 16 15 16 5 8 40
Practice
1: 2: 3: 4: 4x 2 9 7 2 6y 3x 5 18x 2 19 11x 5x 4y 9 3
Solutions
1: 2: 4x 2 8x 9 7 63 2 6y 2 6y 2 2y 4y 3x 5 3x 5 x 5 5x
3: 4:
CHAPTER 2 Introduction to Variables
18x 2 18x 2 18 2 36 19 11x 19 11x 19 11 209
5x 4y 20xy 9 3 27 At times, especially in calculus, you might need to write a fraction as a product of two fractions or of one fraction and a whole number or of one fraction and a variable The steps you will follow are the same as in multiplying fractions only in reverse
Examples
3 3 1 3 1 1 3 4 1 4 1 4 4 (This expression is different from 3 1 3 1 : 4 4 x 1 x 1 x 1 x 3 3 1 3 1 3 3 3 1 3 1 1 3 x 1 x 1 x x 7 7 1 7 1 8x 8 x 8 x 7x 7 x 7 x 8 8 1 8 x 1 1 x 1 1 x 1 2 2 1 2 2 2 1 2 1 1 2 x 1 1 x 1 1 x 1 x 1
Practice
Separate the factor having a variable from the rest of the fraction 1: 4x 5
CHAPTER 2 Introduction to Variables
2: 3: 4: 5: 6: 7: 7y 15 3 4t 11 12x x 3 4 5 7 4x 1 10 2x 1
Solutions
1: 2: 3: 4: 5: 6: 7: 4x 4 x 4 x 4 x 5 5 1 5 1 5 7y 7 y 7 y 7 y 15 15 1 15 1 15 3 3 1 3 1 4t 4 t 4 t 11 11 1 11 1 12x 12 x 12 x x 3 1 x 3 1 x 3 4 4 1 4 5 5 1 5 1 7 4x 1 7 4x 1 7 4x 1 10 10 1 1 10 2x 1 1 2x 1 2x 1
CHAPTER 2 Introduction to Variables
Fraction Division and Compound Fractions
Division of fractions with variables can become multiplication of fractions by inverting the second fraction Because compound fractions are really only fraction division problems, rewrite the compound fraction as fraction division then as fraction multiplication
Example
4 5 x 3
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