Word Problems to Expressions - SSAT Middle Level Quantitative

1. What algebraic expression represents "$3$ fewer than the number of apples $a$"?

   $a-3$. Subtracts 3 from $a$ to express having three fewer items.

2. What algebraic expression represents "the sum of the squares of $x$ and $y$"?

   $x^2+y^2$. Adds the square of $x$ to the square of $y$, applying the exponent to each variable separately.

3. What algebraic expression represents "$5$ divided by a number $x$"?

   $\frac{5}{x}$. Divides 5 by $x$ to represent the specified order of division.

4. What algebraic expression represents "the difference of $p$ and $q$"?

   $p-q$. Subtracts $q$ from $p$ to denote the difference, with $p$ as the minuend.

5. What algebraic expression represents "the product of $m$ and $n$"?

   $mn$. Multiplies $m$ and $n$ directly, as juxtaposition implies multiplication.

6. What algebraic expression represents "twice the difference of $x$ and $3$"?

   $2(x-3)$. Multiplies the difference of $x$ and 3 by 2, grouping the subtraction in parentheses.

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

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

8. What algebraic expression represents "twice the sum of $a$ and $b$"?

   $2(a+b)$. Multiplies the sum of $a$ and $b$ by 2, using parentheses to group the addition first.

9. What algebraic expression represents "the sum of twice $a$ and $b$"?

   $2a+b$. Adds $b$ to twice $a$, prioritizing the multiplication before addition.

10. What algebraic expression represents "the difference of twice $x$ and $3$"?

    $2x-3$. Subtracts 3 from twice $x$, prioritizing multiplication before subtraction.

11. What algebraic expression represents "$4$ more than twice a number $k$"?

    $2k+4$. Adds 4 to twice $k$, performing multiplication before addition.

12. What algebraic expression represents "one third of the sum of $x$ and $9$"?

    $\frac{x+9}{3}$. Divides the sum of $x$ and 9 by 3, grouping the addition within parentheses.

13. What algebraic expression represents "$p$ subtracted from $q$"?

    $q-p$. Subtracts $p$ from $q$, reversing the order for the specified subtraction.

14. What algebraic expression represents "half of a number $t$"?

    $\frac{t}{2}$. Divides $t$ by 2 to represent half the value of the variable.

15. What algebraic expression represents "$q$ subtracted from $p$"?

    $p-q$. Subtracts $q$ from $p$, following the order specified in subtraction.

16. What algebraic expression represents "the ratio of $a$ to $b$"?

    $\frac{a}{b}$. Divides $a$ by $b$ to denote the ratio, with $a$ as the numerator.

17. What algebraic expression represents "$y$ decreased by $6$"?

    $y-6$. Subtracts 6 from $y$ to indicate the variable decreased by a constant.

18. What algebraic expression represents "twice a number $k$ increased by $4$"?

    $2k+4$. Increases twice $k$ by 4, equivalent to adding after multiplying.

19. What algebraic expression represents "$4$ less than twice a number $k$"?

    $2k-4$. Subtracts 4 from twice $k$ to indicate a decrease after multiplication.

20. What algebraic expression represents "$6$ decreased by $y$"?

    $6-y$. Subtracts $y$ from 6 to represent the decrease in the specified order.

21. What algebraic expression represents "the square of the sum of $x$ and $2$"?

    $(x+2)^2$. Squares the sum of $x$ and 2, using parentheses to apply the exponent to the entire binomial.

22. What algebraic expression represents "three times a number $y$"?

    $3y$. Multiplies the variable $y$ by 3 to represent tripling the value.

23. What algebraic expression represents "the quotient of $x$ and $5$"?

    $\frac{x}{5}$. Divides $x$ by 5 to express the quotient with $x$ as the dividend.

24. What algebraic expression represents "$4$ increased by twice a number $k$"?

    $4+2k$. Adds twice $k$ to 4, using commutative property of addition.

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

    $x-7$. Subtracts 7 from the variable $x$ to indicate a decrease by seven.

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