Grade 7 quiz: writing algebraic expressions from real-world scenarios

📚 Quick Study Guide

• 🔢 Variable: A letter (like $x$ or $y$) that represents an unknown number.
• ➕ Addition: Look for words like 'sum', 'plus', 'increased by', 'more than'. Example: 'A number increased by 5' translates to $x + 5$.
• ➖ Subtraction: Look for words like 'difference', 'minus', 'decreased by', 'less than'. Example: 'A number decreased by 3' translates to $x - 3$.
• ✖️ Multiplication: Look for words like 'product', 'times', 'multiplied by'. Example: 'Twice a number' translates to $2x$.
• ➗ Division: Look for words like 'quotient', 'divided by'. Example: 'A number divided by 4' translates to $\frac{x}{4}$.
• 💡 'Less than' Trick: When you see 'less than,' reverse the order. For example, '6 less than a number' translates to $x - 6$, not $6 - x$.

✍️ Practice Quiz

1. What algebraic expression represents "seven more than a number"?
1. $7x$
2. $x - 7$
3. $x + 7$
4. $\frac{x}{7}$
2. What algebraic expression represents "the product of a number and twelve"?
1. $x + 12$
2. $x - 12$
3. $\frac{x}{12}$
4. $12x$
3. What algebraic expression represents "the quotient of a number and five"?
1. $5x$
2. $x - 5$
3. $x + 5$
4. $\frac{x}{5}$
4. What algebraic expression represents "nine less than a number"?
1. $9 - x$
2. $9x$
3. $x - 9$
4. $x + 9$
5. What algebraic expression represents "twice a number, plus three"?
1. $2(x + 3)$
2. $2x + 3$
3. $3x + 2$
4. $2x - 3$
6. What algebraic expression represents "a number divided by six, minus one"?
1. $\frac{x}{6} + 1$
2. $\frac{x - 1}{6}$
3. $\frac{x}{6} - 1$
4. $\frac{6}{x} - 1$
7. What algebraic expression represents "five times the sum of a number and two"?
1. $5x + 2$
2. $5 + x + 2$
3. $5(x + 2)$
4. $5x + 10x$