Word Problems to Expressions - ISEE Upper Level Quantitative Reasoning

1. What algebraic expression represents "one half of a number $x$"?

   $\frac{1}{2}x$. Multiplies x by one-half to represent half the value.

2. What algebraic expression represents "five more than a number $x$"?

   $x + 5$. Adds 5 to the variable x to express an increase by five units.

3. What algebraic expression represents "$x$ is at least $10$"?

   $x \ge 10$. Uses greater than or equal to show x is 10 or more.

4. What algebraic expression represents "the product of $x$ and $y$"?

   $xy$. Multiplies x and y to express their product.

5. What algebraic expression represents "seven less than a number $x$"?

   $x - 7$. Subtracts 7 from x to indicate a reduction by seven.

6. What algebraic expression represents "twice the sum of $x$ and $5$"?

   $2(x + 5)$. First adds x and 5, then multiplies by 2 to double the sum.

7. What algebraic expression represents "the average of $x$ and $y$"?

   $\frac{x + y}{2}$. Divides the sum of x and y by 2 to find their mean.

8. What algebraic expression represents "$x$ divided by $y$"?

   $\frac{x}{y}$. Divides x by y to represent the ratio.

9. What algebraic expression represents "three times a number $x$"?

   $3x$. Multiplies x by 3 to denote tripling the value.

10. What algebraic expression represents "$12$ less than $x$"?

    $x - 12$. Subtracts 12 from x to show a decrease by 12.

11. What algebraic expression represents "a number $x$ increased by $15\%$"?

    $x + 0.15x$. Adds 15% of x to x itself to show the increase.

12. What algebraic expression represents "$7$ divided by $x$"?

    $\frac{7}{x}$. Divides 7 by x to express the division.

13. What algebraic expression represents "the sum of $x$ and $12$"?

    $x + 12$. Combines x and 12 through addition to form their total.

14. What algebraic expression represents "the quotient of $x$ and $7$"?

    $\frac{x}{7}$. Divides x by 7 to form the quotient with x as numerator.

15. What algebraic expression represents "the sum of twice $x$ and $5$"?

    $2x + 5$. Doubles x and then adds 5 to form the sum.

16. What algebraic expression represents "$3$ less than the square of $x$"?

    $x^2 - 3$. Subtracts 3 from the square of x to decrease it by 3.

17. What algebraic expression represents "the difference between $x$ and $12$"?

    $x - 12$. Represents the subtraction of 12 from x as the difference.

18. What algebraic expression represents "$15\%$ of a number $x$"?

    $0.15x$. Multiplies x by 0.15 to calculate 15% of the value.

19. What algebraic expression represents "$x$ is $4$ less than $y$"?

    $x = y - 4$. Sets x equal to y minus 4 to show it is 4 less.

20. What algebraic expression represents "$x$ is no more than $10$"?

    $x \le 10$. Uses less than or equal to indicate x does not exceed 10.

21. What algebraic expression represents "$x$ is between $3$ and $8$, inclusive"?

    $3 \le x \le 8$. Bounds x between 3 and 8 inclusive with inequalities.

22. What algebraic expression represents "$x$ decreased by $20\%$"?

    $0.8x$. Multiplies x by 0.8 to subtract 20% from x.

23. What algebraic expression represents "$5$ more than twice $x$"?

    $2x + 5$. Increases twice x by adding 5.

24. What algebraic expression represents "the sum of the squares of $x$ and $3$"?

    $x^2 + 3^2$. Adds the square of x to the square of 3.

25. What algebraic expression represents "the square of the sum of $x$ and $3$"?

    $(x + 3)^2$. Squares the sum of x and 3 as a whole.

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