Skill: Translate algebraic expressions into words

An algebraic expression is a mathematical phrase, not a complete sentence. To translate it into words:

1. Identify the variable, which stands for an unknown number.
2. Look for parentheses to find grouped quantities.
3. Translate the operations in the order they appear.
4. Be careful with subtraction: the order matters.

Example: Translate

$$4(x+3)-7$$

Step 1: Read the parentheses.

The expression $x+3$ means the sum of a number $x$ and 3.

Step 2: Read the coefficient.

The $4$ next to the parentheses means multiplication:

$$4(x+3)$$

So this means four times the sum of a number $x$ and 3.

Step 3: Read the subtraction.

The expression subtracts 7 from the entire quantity. Add this to the phrase:

four times the sum of a number $x$ and 3, minus 7

Therefore,

$$4(x+3)-7$$

translates to:

Four times the sum of a number and 3, minus 7.

The parentheses are important. Saying “four times the sum” shows that the 4 multiplies both $x$ and 3 inside the parentheses.