Writing Algebraic Expressions - Pre Algebra

1. Write an expression for "the product of 4 and a number $y$."

   $4y$.

2. Write an expression for "the quotient of a number $m$ and 6."

   $\frac{m}{6}$.

3. Why is "5 less than $x$" written $x - 5$ rather than $5 - x$?

   "Less than" reverses the order of the words: begin with $x$ and take 5 away from it.

4. Write an expression for the cost of $n$ tickets at 9 dollars each plus a 4 dollar fee.

   $9n + 4$ dollars.

5. Write an expression for "3 less than twice a number $n$."

   $2n - 3$.

6. Write an expression for "the difference of a number $a$ and 10."

   $a - 10$. The difference is taken in the order given.

7. Write an expression for "5 more than a number $n$."

   $n + 5$.

8. Write an expression for "a number $t$ divided by 2, then increased by 9."

   $\frac{t}{2} + 9$.

9. Write an expression for "7 less than a number $x$."

   $x - 7$. "Less than" means start with $x$ and subtract 7.

10. Write an expression for "twice the sum of a number $x$ and 3."

    $2(x + 3)$. The sum is grouped before it is doubled.

11. Write an expression for "the square of a number $k$, decreased by 1."

    $k^2 - 1$.

12. Write an expression for "8 more than 3 times the number of hours $h$."

    $3h + 8$.

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