EXPRESSIONS AND VARIABLES

In feeding season of summer, a blue whale can eat about 4 tons of food every day. To find about how many tons of food a blue whale can eat in a given number of days, we can multiply the number of days by 4, as shown in the table. 

A numerical expression consists of numbers and operations.

In the table above, the expression 4 ⋅ 10 is a numerical expression. It can also be written as 4 x 10 or 4(10).

variable is letter used to represent one or more numbers. A variable expression consists of numbers, variables and operations. 

One way we can use a variable expression is to generalize a pattern, as shown in the table. The variable expression 4 ⋅ k represents the amount of food a blue whale can eat in 'k' number of days. 

We can also write 4 ⋅ k as '4k'. 

To evaluate a variable expression, substitute a number for each variable and evaluate the resulting numerical expression.

Evaluating a Variable Expression

Example 1 :

Evaluate the expression 4 ⋅ k  when k = 90 to find about how many tons of food a blue whale can eat in a feeding season of 90 days. 

Solution :

=  4 ⋅ k

Substitute 90 for k. 

=  ⋅ 90

Multiply. 

=  360

A blue whale can eat about 360 tons of food in 90 days. 

Evaluating Expressions with Two Variables

Example 2 :

Evaluate the following expression when x = 8 and y = 10.

2x + 3y 

Solution :

=  2x + 3y

Substitute 8 for x and 10 for y.

=  2(8) + 3(10)

Simplify.  

=  16 + 30

=  36

Example 3 :

Evaluate the following expression when x = 4 and y = 5.

xy - 2y 

Solution :

=  xy - 2y

Substitute 4 for x and 5 for y. 

=  (4)(5) - 2(5)

Simplify.  

=  20 - 10

=  10

Writing a Variable Expression

Example 4 :

You are planning 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 in each team. 

Solution :

Let y be the number of players in each team.

The word divide indicate division. 

Number of teams

=

Number of players in league

÷

Number of players in each team

Number of teams  =  120 ÷ y  or  120/y. 

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