6D Words to Algebra Study Guide

Key Vocabulary

Translate — to change words into math symbols (numbers, variables, and operations). (traducir)

Phrase → Expression — a word phrase becomes a math expression (no equals sign).

Sentence → Equation — a word sentence with "is" or "equals" becomes an equation (has = sign).

Operation	Key Words	Example (Words)	Example (Algebra)
Addition (+)	sum, more than, plus, increased by, total	"5 more than x"	x + 5
Subtraction (−)	difference, less than, minus, decreased by, fewer	"7 less than n"	n − 7
Multiplication (×)	product, times, of, twice, double, triple	"the product of 3 and x"	3x
Division (÷)	quotient, divided by, per, split equally	"a number divided by 6"	n ÷ 6

"Twelve decreased by twice a number"
• "decreased by" = subtract
• "twice a number" = 2n
• Answer: 12 − 2n

"5 less THAN x" = x − 5, NOT 5 − x! With "less than," the order is reversed. The variable comes first.
"The product OF 3 AND x" = 3x. "Of" and "and" connect the two things being multiplied.
"Is" or "equals" means =. If you see "is," you are writing an equation, not just an expression.
"More than" and "added to" flip the order too: "8 more than y" = y + 8 (same result either way for addition, but read carefully).

Use n for the variable. Write expressions without spaces (e.g., n+5 or 3n-2).

1. Translate: "the sum of a number and 9"

2. Translate: "4 less than a number"

3. Translate: "triple a number decreased by 7"

4. Translate: "a number divided by 5, plus 2"