EXPRESSIONS AND VARIABLES WORKSHEET

Problem 1 :

Identify the variable in the following expression :

23 + y

Problem 2 :

Compare and contract the expressions 2 + x and 2 + 3.

Problem 3 :

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

2x + 3y

Problem 4 :

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

xy - 2y

Problem 5 :

Let the variable expression 4 ⋅ k represent the amount of food a blue whale can eat in 'k' number of days. 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.

Problem 6 :

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.

Answers

Problem 1 :

Identify the variable in the following expression :

23 + y

Answer :

Variable is a letter used to represent one or more numbers. 'y' is the letter found in the above expression.

So, 'y' is the variable in '23 + y'.

Problem 2 :

Compare and contract the following two expressions :

(2 + x) and (2 + 3)

Answer :

In the first expression (2 + x), we find a number '2' and variable 'x' with binary operation '+'. So, it is a variable expression.

In the second expression (2 + 3), we find only the numbers '2' and '3' with binary operation '+'. So, it is a numerical expression. 

Problem 3 :

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

2x + 3y 

Answer :

=  2x + 3y

Substitute 8 for x and 10 for y.

=  2(8) + 3(10)

Simplify.  

=  16 + 30

=  36

Problem 4 :

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

xy - 2y 

Answer :

=  xy - 2y

Substitute 4 for x and 5 for y. 

=  (4)(5) - 2(5)

Simplify.  

=  20 - 10

=  10

Problem 5 :

Let the variable expression 4 ⋅ k represent the amount of food a blue whale can eat in 'k' number of days. 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. 

Answer :

=  4 ⋅ k

Substitute 90 for k. 

=  ⋅ 90

Multiply. 

=  360

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

Problem 6 :

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. 

Answer :

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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