Test questions for writing algebraic expressions from words

📚 Quick Study Guide

• ➕ Addition: Phrases like "more than," "increased by," "sum," and "plus" indicate addition. For example, "5 more than a number x" translates to $x + 5$.
• ➖ Subtraction: Phrases like "less than," "decreased by," "difference," and "minus" indicate subtraction. Note that "less than" reverses the order. For example, "6 less than a number y" translates to $y - 6$.
• ✖️ Multiplication: Phrases like "times," "product," "multiplied by," and "of" (in some contexts) indicate multiplication. For example, "7 times a number z" translates to $7z$.
• ➗ Division: Phrases like "divided by," "quotient," and "ratio" indicate division. For example, "a number a divided by 3" translates to $\frac{a}{3}$.
• 🔢 Variables: Use letters (like $x$, $y$, $n$) to represent unknown numbers.
• 🔣 Constants: Numbers that don't change are constants (like 2, 5, -10).
• 💡 Key Tip: Break down the word problem into smaller parts and identify the operations and variables.

📝 Practice Quiz

1. What is the algebraic expression for "twice a number plus three"?
   1. $x + 3$
   2. $2x + 3$
   3. $2(x + 3)$
   4. $3x + 2$
2. What is the algebraic expression for "five less than a number"?
   1. $5 - x$
   2. $x - 5$
   3. $5 + x$
   4. $-5x$
3. What is the algebraic expression for "the quotient of a number and four"?
   1. $4x$
   2. $x + 4$
   3. $\frac{x}{4}$
   4. $\frac{4}{x}$
4. What is the algebraic expression for "the product of seven and a number"?
   1. $7 + x$
   2. $7 - x$
   3. $\frac{7}{x}$
   4. $7x$
5. What is the algebraic expression for "ten increased by a number"?
   1. $10x$
   2. $x - 10$
   3. $10 + x$
   4. $\frac{10}{x}$
6. What is the algebraic expression for "three times a number, decreased by two"?
   1. $2 - 3x$
   2. $3(x - 2)$
   3. $3x - 2$
   4. $3(2 - x)$
7. What is the algebraic expression for "half of a number, plus one"?
   1. $\frac{1}{2} + x$
   2. $\frac{x}{2} + 1$
   3. $2x + 1$
   4. $\frac{1}{2}(x + 1)$