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Name _______________________________________ Date __________________ Class __________________ At-Home Practice CHAPTER 2 2A Understanding Variables and Expressions Evaluate each expression to find the missing values in the tables. 1. a a 12 52 64 2. x 5x 11 55 67 12 89 13 Write an expression for each table. 3. 4. w r 18 12 12 6 28 22 14 7 38 32 16 8 5. Is 3x 15 an algebraic expression? __________________________ 6. Evaluate x 20 for x 7. __________________________ 7. Evaluate 12s for s 3. __________________________ Write an algebraic expression for each situation. 8. A watch costs d dollars. How would you write the price of a radio that costs $15 more than the watch? ________________________________________________________________________________________ 9. If you divide n newspapers into 5 equal piles, how many newspapers are in each pile? ________________________________________________________________________________________ Write each phrase as a numerical or algebraic expression. 10. 35 less than p 11. the sum of 52 and 108 _______________________________________ ________________________________________ 12. Write two phrases for the expression d 23. ________________________________________________________________________________________ Answers: 1. 79; 101 2. 60; 65 3. w 6 4. r 2 5. Yes 6. 27 7. 36 8. d + 15 9. n 5 10. p 35 11. 52 108 12. d plus 23; 23 more than d; 23 added to d; the sum of d and 23 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 3 Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ CHAPTER 2 Family Letter 2A Understanding Variables and Expressions Dear Family, Vocabulary The student is learning how to identify and evaluate algebraic expressions. When evaluating algebraic expressions, the student will substitute a value for the variable and then simplify the expression. An example of how to do this is below. These are the math words we are learning: algebraic expression an expression that contains one or more variables and may contain operation symbols constant a quantity that does not change evaluate substitute a number for each variable in an expression and then follow the order of operations variable a letter or symbol that represents a quantity that can change Evaluate the expression to find the missing values in the table. w w • 15 10 150 Substitute the values for w in w • 15. w 10; 10 • 15 150 12 w 12; 12 • 15 180 15 w 15; 15 • 15 225 The missing values are 180 and 225. The student will also learn how to use a table to write an algebraic expression. Write an expression for the table. What pattern do you see? x 48 6 48 8 6 40 5 40 8 5 32 4 32 8 4 Each value for x is being divided by 8, so the expression for this table is x 8. An important part of solving algebraic word problems is knowing what action or operation to perform. The table below pairs each action to its corresponding operation. Action Put together or combine Find how much more or less Put together groups of equal parts Separate into equal groups Operation Add Subtract Multiply Divide The student will analyze word problems and connect each action to its operation. Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 1 Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ CHAPTER 2 Family Letter 2A Understanding Variables and Expressions continued There are several different ways to describe each operation. Words • sum • plus • added to • more than • minus • take away • difference of • less than • times • multiplied by • the product of • divided by • the quotient of Operation Examples Addition 32 plus 5 32 5 x 15 15 added to x Subtraction s 12 12 less than s 11 5 11 minus 5 12a 12 times a Multiplication 3 • 6 the product of 3 and 6 125 5 the quotient of Division 125 and 5 n 3 n divided by 3 The student is learning to translate words into math expressions and math expressions into words. Write each phrase as a numerical or algebraic expression. A. the product of 14 and x 14x B. the difference of 127 and 115 127 115 Write two phrases for the expression 45x. the product of 45 and x 45 times x Reviewing these math terms with the student will help reinforce his or her math vocabulary. Sincerely, Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 2 Holt McDougal Mathematics Name _______________________________________ Date __________________ Class __________________ CHAPTER 2 Family Fun Mind-Reading Mathematics If you have ever wanted to impress your friends and family by being able to read their minds, now is your chance! Just follow these simple directions for two amazing tricks to become a Mind-Reading Mathematician. Game 1 Game 2 I Can Guess Your Answer I Know What You’re Thinking 1. Think of a number. 1. Think of a number between 1 and 9. 2. Double it. 2. Multiply that number by 7. 3. Add 6. 3. Multiply that product by 3. 4. Divide it by 2. 4. Multiply that product by 11. 5. Subtract your original 5. Multiply that product by 37. number from the quotient. 6. Multiply that product by 13. What is your answer every single time? What is your answer every single time? _______________________________ ________________________________ Answers: Game 1: 3 Game 2: Six digit number with the same digit repeated. Sample: 111,111 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 4 Holt McDougal Mathematics