Operation Clue Words Cheat Sheet
Algebra & Pre-Algebra Quick Reference Guide
MATH TRANSLATION CHEAT SHEET
Keywords and clues for operations, algebraic equations, and inequalities
Keep in Binder /
Desk Reference
➕ ADDITION (+)
Combine / Increase
• Sum
• Plus
• Increased by
• More than
• Total of
• Combined
• In all / Altogether
• Gain / Deposit
• Added to
• Perimeter (sum of sides)
Example: "5 more than a number" n + 5
➖ SUBTRACTION (-)
Difference / Reduce
• Difference
• Minus
• Decreased by
• Less than ⚠️
• Subtracted from ⚠️
• Fewer than ⚠️
• Diminished by
• Loss / Deduct
• Take away / Remains
• Exceeds / How much more
Example: "4 less than a number" n - 4
✖️ MULTIPLICATION (·)
Scaling / Equal Groups
• Product
• Times
• Of (fraction/%)
• Multiplied by
• Double (2x)
• Triple (3x)
• Per / Each (rate)
• As much / At this rate
• Twice / Thrice
• Area (length × width)
Example: "Half of a number" \(\frac{1}{2}n\)
➗ DIVISION (÷)
Separating / Sharing
• Quotient
• Divided by
• Split / Shared equally
• Ratio of
• Per / Each (unit rate)
• Out of (fractions)
• Half of / Third of
• Cut into equal parts
• Goes into
• Average / Mean
Example: "The quotient of x and 3" \(\frac{x}{3}\)
🚨 Order Switch Alert: "Turnaround Words" FLIP THE ORDER!
When you see "less than", "fewer than", "subtracted from", or "added to", write the second term first!
"8 less than y" → y - 8 (NOT 8 - y) "10 subtracted from k" → k - 10
Equals & Grouping Rules (=) and ( )
🟰 The Equal Sign (=):
• Is / Are / Was / Were
• Equals / Is equal to
• Yields / Produces
• Amounts to / Results in
• The same as
• Gives / Totals
📦 Grouping Words (Use Parentheses!):
Words like "the quantity of" or "the sum/difference of ... times" mean perform this operation first in parentheses:
"Twice the sum of x and 4" 2(x + 4)
"5 times the difference of y and 3" 5(y - 3)
Inequality Clue Matrix <, ≤, >, ≥
≤
Less than or equal to
At most • Maximum of • No more than
x ≤ 10
≥
Greater than or equal to
At least • Minimum of • No less than
x ≥ 18
<
Strictly Less Than
Fewer than • Under • Below • Shorter than
x < 5
>
Strictly Greater Than
More than • Exceeds • Over • Above • Older than
x > 12
Pro-Tip 1. Identify unknown (\(x\)) → 2. Circle clue words → 3. Check for turnaround words → 4. Write expression
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