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).
A 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.
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.
= 4 ⋅ 90
Multiply.
= 360
A blue whale can eat about 360 tons of food in 90 days.
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
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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