Variables as unknown quantities, basic notation
Middle School Bridge • 6-8
In arithmetic, you work with specific numbers: 5 + 3 = 8. But what if you want to describe a rule that works for any number? That is where variables come in. A variable is a letter that stands for an unknown or changing quantity. Learning to read and write with variables is like learning a new language -- the language of algebra.
A variable is a symbol (usually a letter like x, y, or n) that represents a number whose value may be unknown or may change. An algebraic expression combines numbers, variables, and operations.
| English Phrase | Algebraic Expression |
|---|---|
| A number plus 5 | x + 5 |
| Three times a number | 3n |
| A number decreased by 7 | y - 7 |
| A number divided by 4 | n⁄4 |
| Twice a number, increased by 3 | 2x + 3 |
In algebra, multiplication is often shown without the × symbol to avoid confusion with the variable x:
Write an expression for: "seven less than three times a number."
To evaluate an expression, substitute the given value for each variable and compute.
Evaluate 4x - 3 when x = 5.
Evaluate 2a + b2 when a = 3 and b = 4.
When substituting a value, use parentheses around the number to keep your work clear and avoid sign errors. Write 4(-2) instead of 4 × -2, which can look confusing.
1. Write an algebraic expression for "the sum of a number and twelve."
n + 12 (or x + 12, or any variable).
2. Write an expression for "five times a number, decreased by 2."
5n - 2.
3. Evaluate 3x + 7 when x = 4.
3(4) + 7 = 12 + 7 = 19.
4. Evaluate 10 - 2y when y = -3.
10 - 2(-3) = 10 + 6 = 16.
5. Evaluate x + 4⁄2 when x = 6.
(6 + 4) / 2 = 10 / 2 = 5.
A variable is a letter representing an unknown or changeable number. Algebraic expressions combine variables, numbers, and operations. Multiplication between a number and a variable is written without a symbol (3n means 3 times n). To evaluate an expression, substitute the given values and compute using the order of operations.