TRANSLATING VERBAL PHRASES
Learn how to convert English words into algebraic expressions. Study the keywords and techniques carefully!
In Math, we often need to change real-life situations into Algebraic Expressions. To do this, we need to know the equivalent Math operation for specific English words.
Memorize these words! They tell you exactly what Math operation to use.
ADDITION (+)
sum, plus, increased by, more than, total
SUBTRACTION (−)
difference, minus, decreased by, less than
MULTIPLICATION (×)
product, times, twice, doubled, of
DIVISION (÷)
quotient, divided by, ratio, per
Read the phrase word-by-word and replace them with Math symbols.
Example 1: "A number x increased by 7"
Step 2: "increased by" → +
Step 3: "7" → 7
Combine: → x + 7
Example 2: "Twice a number y"
Step 2: "a number y" → y
Combine: → 2y
This is the most common mistake! When you see "less than", you must SWITCH the order of the terms. The number that comes AFTER "less than" is subtracted from the number that comes BEFORE it.
Example 3: "5 less than a number n"
Step 2: Because of "less than", switch them! → n, 5
Step 3: Put the minus sign in between.
Result: → n − 5
WARNING: It is NOT 5 - n! The order matters in subtraction.
If a phrase says "the sum of..." or "the difference of..." BEFORE another operation, you need to use parentheses to group them together.
Example 4: "Twice the sum of x and 4"
Step 2: "sum of x and 4" → (x + 4)
Combine: → 2(x + 4)
Example 5: "The sum of a number y and 3, divided by 5"
Step 2: "divided by 5" → ÷ 5
Combine: → (y + 3) / 5 or (y + 3) ÷ 5
Read each verbal phrase carefully. Choose the correct algebraic expression. Good luck!
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