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Expressions and Variables

Learn to evaluate numerical and variable expressions to find solutions to real-world problems. Discover the use of variables in mathematical operations through practical examples.

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Expressions and Variables

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  1. 1.1 Expressions and Variables LESSON Blue Whales During its summer feeding season, a blue whale eats about 4 tons of food every day. To find about how many tons of food a blue whale eats in a given number of days, you can multiply the number of days by 4, as shown in the table.

  2. 1.1 Expressions and Variables LESSON A numerical expression consists of numbers and operations. In the table, the expression 4 • 10 is a numerical expression. It can also be written as 4  10 or 4(10).

  3. 1.1 Expressions and Variables LESSON A numerical expression consists of numbers and operations. In the table, the expression 4 • 10 is a numerical expression. It can also be written as 4  10 or 4(10). A variable is a letter used to represent one or more numbers. A variable expression consists of numbers, variables, and operations.

  4. 1.1 Expressions and Variables LESSON A numerical expression consists of numbers and operations. In the table, the expression 4 • 10 is a numerical expression. It can also be written as 4  10 or 4(10). A variable is a letter used to represent one or more numbers. A variable expression consists of numbers, variables, and operations. To evaluate a variable expression, substitute a number for each variable and evaluate the resulting numerical expression.

  5. 1.1 Expressions and Variables LESSON 1 EXAMPLE Evaluating a Variable Expression Evaluate the expression 4 • d when d=120 to find out about how many tons of food a blue whale eats in a feeding season of 120 days. SOLUTION 4 • d =4 • 120 Substitute 120 for d. = 480 Multiply. ANSWER A blue whale eats about 480 tons of food in 120 days.

  6. 1.1 Expressions and Variables LESSON Study Strategy When you write a variable expression involving multiplication, avoid using the symbol . It may be confused with the variable x.

  7. 1.1 Expressions and Variables LESSON 2 EXAMPLE Evaluating Expressions with Two Variables Evaluate the expression when x=10 and y=4. 10 + 4 x + y = Substitute 10 for x and 4 for y. = 14 Add.

  8. 1.1 Expressions and Variables LESSON 2 EXAMPLE Evaluating Expressions with Two Variables Evaluate the expression when x=10 and y=4. 10 + 4 x + y = Substitute 10 for x and 4 for y. = 14 Add. xy = 10(4) Substitute 10 for x and 4 for y. = 40 Multiply.

  9. 1.1 Expressions and Variables LESSON Writing Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations.

  10. 1.1 Expressions and Variables LESSON 3 EXAMPLE Number of players in league Number of players on each team =  Number of teams 120 p The number of teams is 120  p, or . Evaluating a Variable Expression Baseball You plan to divide the 120 players in a baseball league into teams with the same number of players. Use a verbal model to write a variable expression for the number of teams if you know the number of players on each team. SOLUTION Let p represent the number of players on each team. The word divide indicates division. = 120  p ANSWER

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