Writing and Interpreting Algebraic Expressions

An algebraic expression is a mathematical phrase that contains numbers, operations (like addition or multiplication), and variables. A variable is a letter that represents an unknown or changing value.

Parts of an Expression

To properly read and interpret algebraic expressions, you need to recognize their basic building blocks:

• Terms: The parts of an expression that are separated by addition ($+$) or subtraction ($-$) signs.
• Coefficient: The number that is multiplied by a variable.
• Constant: A fixed number that stands alone, without a variable.

Example: Let's look at the expression $4x + 7$

• The terms are $4x$ and $7$.
• The coefficient is $4$ (because it is multiplying the variable $x$).
• The constant is $7$ (because it is a number on its own).

Translating Words into Math

You can translate everyday word phrases into algebraic expressions by looking for specific clue words that tell you which math operation to use:

• Addition ($+$): sum, more than, increased by, total
• Subtraction ($-$): difference, less than, decreased by, minus
• Multiplication ($\times$): product, times, twice ($2 \times$), triple ($3 \times$)
• Division ($\div$): quotient, divided by, half

Example Problems

1. Write an algebraic expression for "the sum of a number $y$ and 12".

• Clue: "Sum" means addition.
• Expression: $y + 12$

2. Write an expression for "5 less than twice a number $n$".

• Clue 1: "Twice a number $n$" means you multiply $n$ by 2, which is written as $2n$.
• Clue 2: "5 less than" means you must subtract 5 from that amount.
• Expression: $2n - 5$ (Note: Be careful with "less than"! The number being subtracted goes at the end.)