Translating Word Phrases to

Algebraic Expressions:

The key to solving applications!

Exploration One

Choose the algebraic expression that correctly translates the word phrase shown.

What number plus 15 is 22?

• n times 15 equals 22 $n·15=22$
• n divided 15 equals 22 $n÷15=22$
• n minus 15 equals 22 $n-15=22$
• n plus 15 equals 22 $n+15=22$

Exploration Two

Translate the key words "sum", "difference", "product", and "quotient".

The

sum difference product quotient

of what number and 15 is 22?

• n times 15 equals 22 $n·15=22$

• n divided by 15 equals 22 $n÷15=22$

• n minus 15 equals 22 $n-15=22$

• n plus 15 equals 22 $n+15=22$

Exploration Two (continued)

What number

plus added to increased by minus decresed by times divided by multiplied by

15 is 22?

• n times 15 equals 22 $n·15=22$

• n divided by 15 equals 22 $n÷15=22$

• n minus 15 equals 22 $n-15=22$

• n plus 15 equals 22 $n+15=22$

Exploration Three

15

more than less than subtracted from less than twice more than twice

what number is 22?

• n plus 15 equals 22 $n+15=22$
• n minus 15 equals 22 $n-15=22$
• 15 minus n equals 22 $15-n=22$
• n divided by 15 equals 22 $n÷15=22$

• 2 times n plus 15 equals 22 $2n+15=22$
• 2 times n minus 15 equals 22 $2n-15=22$
• n squared plus 15 equals 22 $n^2+15=22$
• n squared minus 15 equals 22 $n^2-15=22$

Correct! You chose addition!

Try again! "More than" translates to an expression with addition.

Correct! You correctly arranged the terms and used subtraction as the operation.

Try again! "Less than" rearranges the order of the terms.

Try again! "Less than" translates to an expression with subtraction.

Try again! "Subtracted from" rearranges the order of the terms.

Try again! "Subtracted from" translates to an expression with subtraction.

Try again! "Less than" does not translate to " the plus sign $+$".

Try again! Twice what number does not translate to " n squared $n^2$".

Try again! "More than" does not translate to " the minus sign $-$".

Once you have become sure of how to translate the words to equations in application problems, the mystery and perceived difficulty of word problems evaporates. Solutions seem not only possible, but easy. Keep practicing translation skills and you may find yourself saying that word problems aren't so bad after all!