Grade 5 Test Questions: Writing Algebraic Expressions from Words

📚 Quick Study Guide

• 🔢 Variable: A symbol (usually a letter like $x$ or $y$) that represents an unknown number.
• ➕ Addition: Words like 'plus', 'more than', 'increased by', 'sum' indicate addition. Example: 'a number plus 5' translates to $x + 5$.
• ➖ Subtraction: Words like 'minus', 'less than', 'decreased by', 'difference' indicate subtraction. Example: 'a number minus 3' translates to $x - 3$.
• ✖️ Multiplication: Words like 'times', 'product', 'multiplied by' indicate multiplication. Example: '6 times a number' translates to $6x$.
• ➗ Division: Words like 'divided by', 'quotient' indicate division. Example: 'a number divided by 2' translates to $\frac{x}{2}$.
• 🧐 Important Note: 'Less than' reverses the order. For example, '4 less than a number' translates to $x - 4$, not $4 - x$.

📝 Practice Quiz

1. What algebraic expression represents "seven more than a number"?
1. $x - 7$
2. $7x$
3. $x + 7$
4. $\frac{x}{7}$
2. Which expression shows "the product of nine and a number"?
1. $9 + x$
2. $9 - x$
3. $\frac{9}{x}$
4. $9x$
3. Translate: "A number decreased by twelve"
1. $12 - x$
2. $x + 12$
3. $x - 12$
4. $12x$
4. What does $\frac{x}{4}$ represent in words?
1. Four more than a number
2. Four less than a number
3. A number divided by four
4. Four times a number
5. "Ten less than a number" can be written as:
1. $10 - x$
2. $10x$
3. $x - 10$
4. $x + 10$
6. Choose the expression for "twice a number plus three"
1. $2(x + 3)$
2. $2x + 3$
3. $2 + 3x$
4. $5x$
7. Which algebraic expression represents "the quotient of a number and six"?
1. $6x$
2. $x - 6$
3. $\frac{6}{x}$
4. $\frac{x}{6}$