📖 What Is Translating?
Algebra uses letters and symbols. English uses words. Translating means converting a sentence written in words into a math expression or equation.
The GED doesn't ask you to invent equations — it asks you to recognize the correct one. That means reading carefully and knowing which words connect to which operations.
Two key definitions:
An expression is a math phrase — it has NO equals sign. Example: 2x + 5
An equation shows two things are equal — it HAS an equals sign. Example: 2x + 5 = 11
The word "is" usually means equals (=). When you see "is" in a translation problem, that's where the equals sign goes.
🔑 Operation Clue Words
Certain words always point to the same operation. Memorize these — they are your translation map.
| Operation |
Clue Words |
Example → Math |
| ➕ Addition |
plus, more than, increased by, sum, total, added to |
x + 7 |
| ➖ Subtraction |
minus, less than, fewer than, decreased by, difference, younger than, below |
x − 5 |
| ✖ Multiplication |
times, product, twice, triple, of, multiplied by |
3x |
| ➗ Division |
divided by, quotient, per, ratio, out of |
x ÷ 4 |
| ² Exponents |
squared, cubed, to the power of |
x² |
⚠️ The Reversal Rule — Most Common GED Trap
This is the #1 translation mistake on the GED. Some subtraction phrases reverse the order of the numbers.
The Reversal Phrases: less than · fewer than · younger than · shorter than · below
When you see "less than," the number that appears first in the sentence actually goes second in the math.
⚠️ Reversal in Action
❌ Wrong
"5 less than x"
5 − x
Wrote it in word order — wrong!
✓ Correct
"5 less than x"
x − 5
Start with x, subtract 5.
Memory trick: "5 less than x" means x is the starting point — you're describing how much LESS than x the answer is. So x goes first: x − 5.
More examples of the reversal rule:
Reversal Example
"3 fewer than a number"
= x − 3 (NOT 3 − x)
Reversal Example
"A child is 8 years younger than her brother"
child's age = b − 8 (NOT 8 − b)
( ) When to Use Parentheses
Some phrases tell you to group things together first before multiplying or dividing. These phrases require parentheses.
Grouping Phrases
the sum of · the difference of · the quantity · the total of
These mean: put parentheses around the group.
Why It Matters
2(x + 4) ≠ 2x + 4
In 2(x + 4), you double the ENTIRE sum. In 2x + 4, you only double x.
🔢 Worked Examples
Example 1 — Basic Translation
"Seven more than a number"
Clue word: "more than" → Addition
Order: "more than a number" means add to the number, no reversal
Answer: x + 7
Example 2 — Reversal
"12 less than a number"
Clue word: "less than" → Subtraction with reversal
The 12 comes first in the sentence — but goes second in the math
Answer: x − 12 (NOT 12 − x)
Example 3 — Multi-Step
"Three more than twice a number"
Step 1: "twice a number" = 2x
Step 2: "three more than" that = add 3
Answer: 2x + 3
Example 4 — Parentheses
"Twice the sum of a number and 9"
Step 1: "the sum of a number and 9" = (x + 9) ← group it
Step 2: "twice" that group = multiply (x + 9) by 2
Answer: 2(x + 9) NOT 2x + 9
Example 5 — Real-World Equation
"A gym charges a $30 sign-up fee plus $25 per month. Write an expression for the total cost after m months."
$30 is a one-time fee (doesn't multiply)
"$25 per month" → per = multiply by m → 25m
Answer: 30 + 25m
Example 6 — Exponent
"4 less than the square of a number"
Step 1: "the square of a number" = x²
Step 2: "4 less than" = subtract 4, with reversal
Answer: x² − 4 (NOT 4 − x²)
🚫 Common Mistakes to Avoid
Mistake 1
Writing "5 less than x" as 5 − x
✓ Correct: x − 5 (reversal rule)
Mistake 2
Writing "twice the sum of x and 4" as 2x + 4
✓ Correct: 2(x + 4) (need parentheses)
Mistake 3
Calling x + 7 an equation
✓ No equals sign → it's an expression
Mistake 4
Treating "per" as addition instead of multiplication
✓ "$25 per month" = 25m (multiply by months)
✏️ Practice Questions