Situations to Expressions - ISEE Middle Level Quantitative Reasoning

1. What algebraic expression represents "$5$ is at least a number $x$"?

   $5 \ge x$. The phrase 'at least' indicates greater than or equal to, so 5 is greater than or equal to x.

2. What algebraic expression represents "the total cost of $x$ items at $5 each plus a $2 fee"?

   $5x + 2$. Multiplying the number of items x by 5 and adding the 2 fee gives the total cost.

3. What algebraic expression represents "$7$ less than a number $x$"?

   $x - 7$. Subtracting 7 from the number x expresses a value that is 7 less than x.

4. What algebraic expression represents "$7$ less than twice a number $x$"?

   $2x - 7$. Multiplying x by 2 and then subtracting 7 gives a value 7 less than twice x.

5. What algebraic expression represents "a number $x$ is less than $12$"?

   $x < 12$. The phrase 'less than' indicates a strict inequality where x is below 12.

6. What algebraic expression represents "twice the difference of a number $x$ and $7$"?

   $2(x - 7)$. The difference between x and 7 is x - 7, which is then multiplied by 2.

7. What algebraic expression represents "$7$ more than a number $x$"?

   $x + 7$. Adding 7 to the number x expresses a value that is 7 greater than x.

8. What algebraic expression represents "the sum of $3$ times a number $x$ and $5$"?

   $3x + 5$. Adding 5 to three times x combines the product 3x with 5.

9. What algebraic expression represents "the perimeter of a rectangle with length $l$ and width $w$"?

   $2l + 2w$. The perimeter is the sum of all sides, doubling the length and width.

10. What algebraic expression represents "the quotient of the sum $x + y$ and $2$"?

    $\frac{x + y}{2}$. Dividing the sum of x and y by 2 gives the quotient.

11. What algebraic expression represents "a number $x$ is at least $5$"?

    $x \ge 5$. The phrase 'at least' means x is greater than or equal to 5.

12. What algebraic expression represents "a number $x$ is no more than $12$"?

    $x \le 12$. The phrase 'no more than' means x is less than or equal to 12.

13. What algebraic expression represents "$4$ more than one-third of a number $x$"?

    $\frac{x}{3} + 4$. One-third of x is x/3, and adding 4 increases it by 4.

14. What algebraic expression represents "the difference of twice a number $x$ and $7$"?

    $2x - 7$. The difference between twice x and 7 is found by subtracting 7 from 2x.

15. What algebraic expression represents "the product of $x$ and the quantity $y - 6$"?

    $x(y - 6)$. Multiplying x by the difference y - 6 groups the operations correctly.

16. What algebraic expression represents "$3$ consecutive integers, starting with $n$"?

    $n,\ n + 1,\ n + 2$. Consecutive integers increase by 1 each time, starting from n.

17. What algebraic expression represents "$5$ more than $3$ times a number $x$"?

    $3x + 5$. Increasing three times x by 5 is equivalent to adding 5 to 3x.

18. What algebraic expression represents "$7$ subtracted from twice a number $x$"?

    $2x - 7$. Subtracting 7 from twice x means first doubling x and then reducing by 7.

19. What algebraic expression represents "$4$ times a number $x$ divided by $3$"?

    $\frac{4x}{3}$. Multiplying x by 4 and dividing by 3 expresses the described operation.

20. What algebraic expression represents "$3$ times the sum of a number $x$ and $5$"?

    $3(x + 5)$. The sum of x and 5 is x + 5, which is then multiplied by 3.

21. What algebraic expression represents "the quotient of a number $x$ and the sum $y + 2$"?

    $\frac{x}{y + 2}$. Dividing x by the sum of y and 2 forms the quotient.

22. What algebraic expression represents "a number $x$ divided by $3$, then increased by $4$"?

    $\frac{x}{3} + 4$. Dividing x by 3 and then adding 4 follows the sequence of operations.

23. What algebraic expression represents "$6$ less than the product of $x$ and $y$"?

    $xy - 6$. Subtracting 6 from the product of x and y decreases it by 6.

24. What algebraic expression represents "twice a number $x$ decreased by $7$"?

    $2x - 7$. Decreasing twice the number x by 7 is achieved by multiplying x by 2 and subtracting 7.

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