Sample of words used to represent mathematical operations:
| ADD | SUBTRACT | MULTIPLY | DIVIDE |
|---|---|---|---|
| add | subtract | multiplied by | divided by |
| sum | difference | product of | quotient |
| increased by | decreased by | times | per |
| more than* | less than* | double | split equally |
| exceeds | minus | triple | ratio of |
| plus | take away | twice of | divided among |
| total | reduced by | grouped | each |
| gain | loss | out of | |
| deposit | withdraw |
Note: Phrases like “less than” and “more than” require reversing the usual order of terms in translation. For example: “5 less than $x$” means $x - 5$.
| Statement | Algebraic Expression |
|---|---|
| Seven increased by five times a number. | $$7 + 5x$$ |
| Ten less than three times a number. | $$3x - 10$$ |
| Six times a number, increased by 4. | $$6x + 4$$ |
| The product of 2, and a number decreased by 6. | $$2(x - 6)$$ |
| A number used as a factor of itself 4 times. | $$x^4$$ |
| Four times a number, divided by 8 equals 12. | $$\frac{4x}{8} = 12$$ |
| 12 less than the quotient of a number and 3 is zero. | $$\frac{x}{3} - 12 = 0$$ |
| 15 more than twice the product of a number and 5 is 55. | $$2 \cdot 5x + 15 = 55$$ |
| A fourth of the sum of a number and 3. | $$\frac{x + 3}{4}$$ |
