Introduction to Multilingual Retrieval Augmented Generation (RAG)
PreAlgebra 1.1
1. 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. Expressions and Variables 4 • d d 4 • 10 10 4 • 2 2 4 • 1 1 Tons of food eaten Days 1.1 LESSON
2. 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 ). Expressions and Variables 1.1 LESSON
3. A variable is a letter used to represent one or more numbers. A variable expression consists of numbers, variables, and operations. 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 ). Expressions and Variables 1.1 LESSON
4. 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 ). To evaluate a variable expression, substitute a number for each variable and evaluate the resulting numerical expression. A variable is a letter used to represent one or more numbers. A variable expression consists of numbers, variables, and operations. Expressions and Variables 1.1 LESSON
5. Evaluating a Variable Expression = 480 ANSWER A blue whale eats about 480 tons of food in 120 days. Multiply. SOLUTION 4 • d = 4 • 120 Substitute 120 for d . 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. EXAMPLE 1 Expressions and Variables 1.1 LESSON
6. Study Strategy When you write a variable expression involving multiplication, avoid using the symbol . It may be confused with the variable x . Expressions and Variables 1.1 LESSON
7. Evaluating Expressions with Two Variables Evaluate the expression when x = 10 and y = 4 . x + y = Substitute 10 for x and 4 for y . = 14 10 + 4 Add. EXAMPLE 2 Expressions and Variables 1.1 LESSON
8. Evaluating Expressions with Two Variables Evaluate the expression when x = 10 and y = 4 . Substitute 10 for x and 4 for y . x y = Substitute 10 for x and 4 for y . = 40 10 ( 4 ) Add. Multiply. x + y = = 14 10 + 4 EXAMPLE 2 Expressions and Variables 1.1 LESSON
9. 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. Expressions and Variables divided by divided into the quotient of Division times the product of multiplied by of Multiplication Common Words and Phrases that Indicate Operations minus the difference of decreased by fewer than less than subtracted from plus the sum of increased by total more than added to Subtraction Addition 1.1 LESSON
10. 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. = 120 p ANSWER SOLUTION Let p represent the number of players on each team. The word divide indicates division. EXAMPLE 3 Expressions and Variables Number of teams = Number of players in league Number of players on each team The number of teams is 120 p , or . 120 p 1.1 LESSON
