A number added to 7, 2) 3 times a number 7/ce away, 3) Half a number -> cln 1/2 n h/n, 4) 5 more than twice a number

Step 1: Translate each phrase into an algebraic expression.

1. "a number added to 7" Let the number be $x$.

   $$x + 7$$

   The student's work "n-3=13" is an equation, not an expression for "a number added to 7".

2. "3 times a number take away 4" Let the number be $x$. "3 times a number" is $3x$. "take away 4" means subtract 4.

   $$3x - 4$$

   The student's work "3n - 4" is correct if $n$ represents the number.

3. "Half a number" Let the number be $x$. "Half a number" means dividing the number by 2.

   $$\frac{x}{2} \quad \text{or} \quad \frac{1}{2}x$$

   The student's work "1/2n n/" correctly shows $\frac{1}{2}n$ or $\frac{n}{2}$.

4. "5 more than twice a number" Let the number be $x$. "twice a number" is $2x$. "5 more than" means add 5.

   $$2x + 5$$

   The student's work "5p-n" is incorrect.

Here are the correct algebraic expressions:

1. A number added to 7: $\boxed{x + 7}$
2. 3 times a number take away 4: $\boxed{3x - 4}$
3. Half a number: $\boxed{\frac{x}{2}}$
4. 5 more than twice a number: $\boxed{2x + 5}$