The most important skill in algebra is learning how to turn English sentences into mathematical expressions. This allows us to solve real-world problems using math.
Here are some common phrases and their symbolic counterparts:
| English Statement | Symbolic Form |
| The sum of $a$ and $b$ | $a + b$ |
| The subtraction of $b$ from $a$ | $a – b$ |
| The product of $2$ and $x$ | $2 \times x = 2x$ |
| Divide $x$ by $2$ | $\frac{x}{2}$ |
| $6$ more than $x$ | $x + 6$ |
| $5$ decreased by $x$ | $5 – x$ |
| $5$ times $x$ | $5x$ |
| $40$ divided by $x$ | $\frac{40}{x}$ |
| $5$ times $x$ added to $3$ times $y$ | $5x + 3y$ |
| The subtraction of $2x$ from $3$ | $3 – 2x$ |
| $4$ less than half of $x$ | $\frac{x}{2} – 4$ |
“More than” or “Sum” usually indicates addition ($+$).
“Less than” or “Decreased by” usually indicates subtraction ($-$).
“Product” or “Times” indicates multiplication ($\times$).
“Quotient” or “Divided by” indicates division ($\div$ or a fraction bar).
Watch the Order: In subtraction, “subtract $b$ from $a$” means $a$ comes first ($a – b$). This is a common spot where students make mistakes!
In the continuation of our series on Algebraic Expressions, we will explore the essential building blocks that make up these expressions: terms, factors, coefficients, and how to combine them.