Real-World Examples: How to Translate Math Expressions into Words

📚 Quick Study Guide

• ➕ Addition: Represented by words like 'plus,' 'added to,' 'the sum of,' 'more than,' and 'increased by.'
• ➖ Subtraction: Represented by words like 'minus,' 'subtracted from,' 'the difference of,' 'less than,' and 'decreased by.'
• ✖️ Multiplication: Represented by words like 'times,' 'multiplied by,' 'the product of,' and 'of.'
• ➗ Division: Represented by words like 'divided by,' 'the quotient of,' and 'per.'
• 🟰 Equality: Represented by words like 'equals,' 'is,' 'is equal to,' and 'is the same as.'
• 🔢 Variables: Represented by letters like $x$, $y$, and $z$. Think of them as placeholders for unknown numbers.
• 📝 Exponents: $x^2$ is "x squared," $x^3$ is "x cubed," and $x^n$ is "x to the power of n."
• 📐 Fractions: $\frac{1}{2}$ is "one-half," $\frac{3}{4}$ is "three-fourths," and $\frac{a}{b}$ is "a divided by b."

✍️ Practice Quiz

1. What is the verbal expression for $2x + 5$?
   1. A) Five more than twice a number
   2. B) Two times five plus a number
   3. C) Two plus a number times five
   4. D) Two times a number less than five
2. Which mathematical expression represents 'the quotient of a number and 3'?
   1. A) $3x$
   2. B) $x - 3$
   3. C) $\frac{x}{3}$
   4. D) $x + 3$
3. Translate: 'Seven less than the product of 4 and a number'
   1. A) $7 - 4x$
   2. B) $4x - 7$
   3. C) $4(x - 7)$
   4. D) $7 < 4x$
4. Which of the following is the correct translation of '$x^2 - 9$'?
   1. A) Nine less than a number
   2. B) The difference of a number and nine
   3. C) Nine less than a number squared
   4. D) The square root of a number minus nine
5. What does 'the sum of a number and 10, divided by 2' look like mathematically?
   1. A) $\frac{x}{2} + 10$
   2. B) $\frac{x + 10}{2}$
   3. C) $\frac{10}{2} + x$
   4. D) $\frac{10x}{2}$
6. Express $5(x + 2)$ in words.
   1. A) Five times a number plus two
   2. B) Five times the sum of a number and two
   3. C) Five plus a number times two
   4. D) Five times a number times two
7. How do you translate 'Eight increased by the square of a number'?
   1. A) $(8 + x)^2$
   2. B) $8x^2$
   3. C) $8 + x^2$
   4. D) $(8x)^2$