Find which of the following expressions are algebraic expressions and which are arithmetic expressions.
a. `3 xx (5 + y)`
b. `12 - (5 - 3)`
c. ` 3p - 22`
d. `5-(3)/(2) (x - 5)`
e. ` 11 xx (12 div 3)`

Answer

To determine whether each expression is an algebraic expression or an arithmetic expression, we need to identify if they contain variables (like x, y, or p) or if they consist solely of numbers and arithmetic operations.

Let's analyze each expression step by step:

### Step 1: Analyze Expression a: `3 xx (5 + y)`

- This expression contains the variable `y`.
- Since it includes a variable, it is classified as an **algebraic expression**.

### Step 2: Analyze Expression b: `12 - (5 - 3)`

- This expression consists only of numbers and arithmetic operations.
- There are no variables present, so it is classified as an **arithmetic expression**.

### Step 3: Analyze Expression c: `3p - 22`

- This expression contains the variable `p`.
- Since it includes a variable, it is classified as an **algebraic expression**.

### Step 4: Analyze Expression d: `5 - (3)/(2) (x - 5)`

- This expression contains the variable `x`.
- Since it includes a variable, it is classified as an **algebraic expression**.

### Step 5: Analyze Expression e: `11 xx (12 div 3)`

- This expression consists only of numbers and arithmetic operations.
- There are no variables present, so it is classified as an **arithmetic expression**.

### Summary of Classifications:
- a. `3 xx (5 + y)` - Algebraic Expression
- b. `12 - (5 - 3)` - Arithmetic Expression
- c. `3p - 22` - Algebraic Expression
- d. `5 - (3)/(2) (x - 5)` - Algebraic Expression
- e. `11 xx (12 div 3)` - Arithmetic Expression