Word Problems to Expressions - SSAT Upper Level Quantitative

1. What is the algebraic expression for "$15$ percent of a number $x$"?

   $0.15x$. 15 percent means multiplying x by 0.15 to find the portion.

2. What is the algebraic expression for "$6$ more than the square of a number $x$"?

   $x^2+6$. Adding 6 to the square of x expresses '6 more than x squared'.

3. What is the algebraic expression for "$5$ divided by a number $x$"?

   $\frac{5}{x}$. Dividing 5 by x gives the result of 5 split by x.

4. What is the algebraic expression for "$x$ is no more than $10$"?

   $x\le 10$. 'No more than 10' means x is less than or equal to 10.

5. What is the algebraic expression for "the sum of twice $x$ and $3$"?

   $2x+3$. Summing twice x and 3 means multiplying x by 2 before adding 3.

6. What is the algebraic expression for "a number $x$ decreased by $9$"?

   $x-9$. Decreasing x by 9 requires subtracting 9 from x.

7. What is the algebraic expression for "$9$ less than a number $x$"?

   $x-9$. '9 less than x' means subtracting 9 from x.

8. What is the algebraic expression for "the square of the sum of $x$ and $2$"?

   $(x+2)^2$. Squaring the sum requires adding x and 2 before raising to the power of 2.

9. What is the algebraic expression for "a number $x$ divided by $5$"?

   $\frac{x}{5}$. Dividing x by 5 expresses x split into 5 equal parts.

10. What is the algebraic expression for "the sum of the squares of $x$ and $2$"?

    $x^2+2^2$. Summing the squares means squaring x and 2 separately before adding.

11. What is the algebraic expression for "$5$ less than three times a number $x$"?

    $3x-5$. Subtracting 5 from three times x represents '5 less than three times x'.

12. What is the algebraic expression for "$x$ increased by $20\%$"?

    $1.2x$. Increasing by 20% means multiplying by 1.2 to include the original plus the increase.

13. What is the algebraic expression for "the sum of a number $x$ and $7$"?

    $x+7$. The sum indicates addition of the number x and 7.

14. What is the algebraic expression for "three times the difference of $x$ and $5$"?

    $3(x-5)$. Three times the difference means subtracting 5 from x first, then multiplying by 3.

15. What is the algebraic expression for "$x$ decreased by $20\%$"?

    $0.8x$. Decreasing by 20% means multiplying by 0.8 to retain 80% of the original.

16. What is the algebraic expression for "the product of $x$ and $y$"?

    $xy$. The product is found by multiplying x and y.

17. What is the algebraic expression for "$6$ more than a number $x$ squared"?

    $x^2+6$. Adding 6 to x squared captures the increase after squaring.

18. What is the algebraic expression for "one-half of a number $x$"?

    $\frac{1}{2}x$. One-half of x is equivalent to multiplying x by $\frac{1}{2}$.

19. What is the algebraic expression for "the quotient of $x$ and $y$"?

    $\frac{x}{y}$. The quotient means dividing x by y.

20. What is the algebraic expression for "$4$ times a number $x$"?

    $4x$. Multiplying 4 by x represents 4 times the number.

21. What is the algebraic expression for "the average of $x$ and $y$"?

    $\frac{x+y}{2}$. The average is the sum of x and y divided by 2.

22. What is the algebraic expression for "$3$ more than twice a number $x$"?

    $2x+3$. Adding 3 to twice x captures '3 more than twice x'.

23. What is the algebraic expression for "$x$ is at least $10$"?

    $x\ge 10$. 'At least 10' indicates x is greater than or equal to 10.

24. What is the algebraic expression for "$9$ decreased by a number $x$"?

    $9-x$. Decreasing 9 by x means subtracting x from 9, reversing the order.

25. What is the algebraic expression for "twice the sum of $x$ and $3$"?

    $2(x+3)$. Twice the sum requires adding x and 3 first, then multiplying by 2.

Study these flashcards