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CHAPTER 2 Introduction to Variables
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Adding and Subtracting Fractions with Variables
When adding or subtracting fractions with variables, treat the variables as if they were prime numbers
Examples
6 y 6 4 y 25 24 25y 24 25y 25 4 25 4 4 25 100 100 100
CHAPTER 2 Introduction to Variables
2t 14 2t 11 14 5 22t 70 22t 70 15 33 15 11 33 5 165 165 165 18 3 18 4 3 x 72 3x 72 3x x 4 x 4 4 x 4x 4x 4x 9 5 16t 12 16t 2 2 2 2 t and 12 2 2 3 so the LCD 2 2 2 2 3 t 48t 48t 16t 3 and 48t 12 4t 9 5 9 3 5 4t 27 20t 27 20t 16t 12 16t 3 12 4t 48t 48t 48t 71 13 84 30x 84 2 2 3 7 and 30x 2 3 5 x LCD 2 2 3 5 7 x 420x and 420x 84 5x and 420x 30x 14 71 13 71 5x 13 14 355x 182 355x 182 84 30x 84 5x 30x 14 420x 420x 420x
Practice
Do not try to reduce your solutions We will learn how to reduce fractions like these in a later chapter 1: 2: 3: 4: 4 2x 15 33 x 7 48 30 3 4 x 25 2 6 45x 35
CHAPTER 2 Introduction to Variables
5: 6: 7: 8: 9: 10: 11 7 150x 36 2 3 21x 98x 1 5 12x 9y 19 1 51y 6x 7x 2 24y 15y 3 2 14y 35x
Solutions
1: 2: 3: 4: 5: 6: 7: 8: 4 2x 4 11 2x 5 44 10x 44 10x 15 33 15 11 33 5 165 165 165 x 7 x 5 7 8 5x 56 5x 56 48 30 48 5 30 8 240 240 240 3 4 3 25 4 x 75 4x 75 4x x 25 x 25 25 x 25x 25x 25x 2 6 2 7 6 9x 14 54x 14 54x 45x 35 45x 7 35 9x 315x 315x 315x 11 7 11 6 7 25x 66 175x 66 175x 150x 36 150x 6 36 25x 900x 900x 900x 2 3 2 14 3 3 28 9 37 21x 98x 21x 14 98x 3 294x 294x 294x 1 5 1 3y 5 4x 3y 20x 3y 20x 12x 9y 12x 3y 9y 4x 36xy 36xy 36xy 19 1 19 2x 1 17y 38x 17y 38x 17y 51y 6x 51y 2x 6x 17y 102xy 102xy 102xy
9: 10:
CHAPTER 2 Introduction to Variables
7x 2 7x 5 2 8 35x 16 35x 16 24y 15y 24y 5 15y 8 120y 120y 120y 3 2 3 5x 2 2y 15x 4y 15x 4y 14y 35x 14y 5x 35x 2y 70xy 70xy 70xy
Word Problems
Often the equations used to solve word problems should have only one variable, and other unknowns must be written in terms of one variable The goal of this section is to get you acquainted with setting your variable equal to an appropriate unknown quantity, and writing other unknown quantities in terms of the variable
Examples
Andrea is twice as old as Sarah Because Andrea s age is being compared to Sarah s, the easiest thing to do is to let x represent Sarah s age: Let x Sarah s age Andrea is twice as old as Sarah, so Andrea s age 2x We could have let x represent Andrea s age, but we would have to re-think the statement as Sarah is half as old as Andrea This would mean Sarah s age would be represented by 1 x 2 John has eight more nickels than Larry has The number of John s nickels is being compared to the number of Larry s nickels, so it is easier to let x represent the number of nickels Larry has Let x the number of nickels Larry has x 8 the number of nickels John has A used car costs $5000 less than a new car
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