Here’s how you can write algebraic expressions or equations for the given statements:

1. The product of seven and 16:
   Algebraic expression: $7 \cdot 16$ or $112$ (simplified).

2. Four times a number, $n$, increased by eight:
   Algebraic expression: $4n + 8$.

3. Sixteen less than a number, $x$, is three more than $y$:
   Equation: $x - 16 = y + 3$.

4. Ten decreased by $x$ is fifteen decreased by $n$:
   Equation: $10 - x = 15 - n$.

5. Fifty is twelve subtracted from $x$:
   Equation: $50 = x - 12$.

6. Twice the sum of $x$ and $y$:
   Algebraic expression: $2(x + y)$.

7. Sixteen is the product of eight and three times $z$:
   Equation: $16 = 8 \cdot (3z)$ or $16 = 24z$ (simplified).

8. Twice the difference of $x$ and $y$:
   Algebraic expression: $2(x - y)$.

9. The quotient of eleven and $y$ is seven minus $x$:
   Equation: $\frac{11}{y} = 7 - x$.

10. Five times the difference of nine and $x$:
    Algebraic expression: $5(9 - x)$.

Let me know if you need further details, clarifications, or explanations!

5 Related Questions:

1. How would the expressions change if the variables were squared?
2. How do you simplify complex expressions involving fractions like $\frac{11}{y} = 7 - x$?
3. Can you convert these equations into verbal descriptions?
4. How do you solve for one variable in equations like $x - 16 = y + 3$?
5. How would the expressions change if terms like "increased" or "decreased" were reversed?

One Tip:

Always carefully analyze the relationship between variables and operations in word problems to translate them accurately into algebraic expressions or equations.