Variable
In short: Variable names a letter, such as n, standing in for an amount that may take many values or hasn’t been found yet, as in the cost 15n of n concert tickets.
6th GradeAlgebra6.EE.A.2
What is Variable?
Think of a variable as a placeholder with a name. Instead of writing a separate calculation for 1 ticket, 2 tickets and 3 tickets, you write one rule using a letter and let it take whatever value the situation needs.
Precisely, a variable such as \(n\), \(t\) or \(x\) represents a quantity whose value may vary within a stated set of numbers, or an unknown number to be found. Replacing it with a number is called substituting and gives a single value for the expression.
How to spot it
- A rule needs to work for any number of tickets, hours or items, not just one case.
- A letter appears in a formula, like \(A = \ell w\) for the area of a rectangle.
- A story hides an unknown amount, such as “a number plus 9 is 24”.
- A table shows an input column whose pattern is the same for every row.
The method
- Choose a letter and say in words what it stands for, including the unit.
- Write the rule using the letter wherever the changing amount belongs, such as \(15n\).
- Substitute a chosen number for the letter, keeping the operations in order.
- Compute and state the result with its unit.
Variable: solved example
Problem
A concert venue in Nashville charges $15 per ticket. Let \(n\) be the number of tickets. Write the cost, then find the cost of 14 tickets.
Solution
The cost in dollars is \(15n\), since each of the \(n\) tickets costs 15.
Substitute \(n = 14\): \(15 \times 14 = 210\). Fourteen tickets cost $210.
Try it
Question 1
Evaluate \(3k + 8\) when \(k = 7\).
Show the answer
\(3 \cdot 7 + 8 = 21 + 8 = 29\).
Question 2
A gym charges $25 to join plus $9 per class. Write the total using c for classes and find it for 6 classes.
Show the answer
Total \(= 25 + 9c\). For \(c = 6\): \(25 + 54 = 79\), so the total is \$79.
Variable vs. Coefficient
The letter is the variable: it can change. The number multiplying it is the coefficient: it stays fixed. In \(15n\), the n is the changing amount and 15 is the fixed price per ticket.
Keep going
Lessons
Worksheets and quizzes
- Writing and Reading Algebraic Expressions – Worksheet
- Writing and Reading Algebraic Expressions – Quiz
- Independent and Dependent Variables – Worksheet
- Independent and Dependent Variables – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Algebra