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Introduction to Algebra

Mathematics, Grade 7

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Study Guide Introduction to Algebra Mathematics, Grade 7

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INTRODUCTION TO ALGEBRA Algebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. When given an algebraic expression, it can be solved by filling in a number for the variable. Word problems can be turned into variable expressions by changing the words to mathematical terms. If an expression has more than one variable expression, it can be combined as long as both have the same variable factor; this is called combining like terms. With algebra, inverse operations can be used to solve equations. Inverse operations are used to isolate a variable. Inverse operations undo an operation; addition is the inverse operation of subtraction and vice versa as well as multiplication being the inverse operation of division and vice versa. How to use algebra: An example of an algebraic expression is 3x + 5. Here the x represents a number that is to be multiplied by three. If x = 2, then the expression equals 3 · 2 + 5 = 11. By filling in 2 for the x, the expression can be solved. Words can be changed into mathematical terms. Look at the following words and translate them into mathematical terms: Ex. Five times a number minus three 5 · n - 3 = 5n - 3 Each word represents a mathematical term. Once this is done, the expression can either be left this way or solved if given a value for n. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Word problems are also changed into variable expressions in the same way. Look at this word problem: Jack rented a movie. The store charged $1.99 for the first day and $.50 for each day after that. If Jack had the movie for d days, what expression could be used to represent the cost of renting a movie in terms of d? $1.99 for the first day and $.50 for each day after that (.50 · d ) the expression is 1.99 + .50d This expression can be solved when 3 (or any other number) is substituted for d, the number of days Jack had the movie. So, 1.99 + .50 · 3 = 1.99 + 1.50 = 3.49 or $3.49. If an expression or equation has more than one variable term, the terms may be combined if the terms have the same variable factor. Example: 5x + 4 - 2x 3x + 4 8x - 6y + x - 2y 9x - 8y To solve an equation using inverse operations, the variable must be isolated first and then the variable can be solved. Example: Solve for x: x + 17 = 27 - 17 -17 x = 10 Seventeen is subtracted from both sides to solve for x. On the left side, the numbers cancel out and on the right side 27 - 17 = 10, the answer. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. Solve if n = 3: 7 - n 2n + 8 4n ÷ 6 2. Translate into an algebraic expression: o Six times a number minus two o A number plus seven 3. Translate the word problem into a variable expression in terms of d, days: Sharon rents a car that costs $89 for the first day and $50 for every day after that. She rents the car for d, days. 4. Combine like terms: 7x - 4 x 11x + 14y - 5x + 2y 6x - 64 3x 5. Solve by using inverse operations: x + 14 = 67 5x = 45 x/2 = 42 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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