Key takeaway: A variable is a letter, such as t, that holds the place of a quantity whose value differs from case to case or is still unknown, so 12 + 0.08t can describe many situations.
Grade 66.EE.A.2Expressions and Equations
Definition of Variable
A variable is a placeholder written as a letter, such as \(t\), \(n\) or \(x\). It holds the spot for a number that may change from one case to the next, or for a number you are trying to find.
Suppose a phone plan costs \$12 a month plus 8 cents per text. The number of texts differs every month, so we let \(t\) stand for it. The cost is then \(12 + 0.08t\) dollars. To use the formula, you replace the letter with a number, which is called substituting. Any letter will do, as long as it means the same thing throughout the problem.
Formula and notation
A letter placed next to a number or another letter means multiplication, so no times sign is needed:
\[5t = 5 \times t \qquad ab = a \times b\]
Writing the number first is the habit: \(5t\), not \(t5\). The multiplication dot or sign is kept only between two numbers, such as \(5 \cdot 3\).
Key facts
- A variable can vary in a formula, or stand for one unknown value in an equation.
- Replacing the letter with a number and calculating is called evaluating.
- The same letter must represent the same number everywhere within one problem.
- Capital and lowercase versions of a letter are treated as different symbols.
Variable example
Rina’s phone plan costs \(12 + 0.08t\) dollars in a month with \(t\) texts. Find her bill when she sends 150 texts, and then when she sends 275.
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Substitute \(t = 150\): \(12 + 0.08 \times 150\).
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Multiply first: \(0.08 \times 150 = 12\), so the bill is \(12 + 12 = 24\).
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Substitute \(t = 275\): \(0.08 \times 275 = 22\), so the bill is \(12 + 22 = 34\).
Her bill is \$24 for 150 texts and \$34 for 275 texts.
Common mistake
Watch out
Ben evaluates \(5t\) for \(t = 4\) and writes 54.
Why it is wrong
He placed the digits side by side as if \(5t\) were a two-digit number. A number touching a letter means multiplication, so \(5t = 5 \times 4 = 20\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Expressions and Equations