State which of the following are algebraic expressions and which are arithmetic expressions.
a. `22x-11a`
b. `6xnp`
c. `12+(5xx4)-15`
d. 5
e. s

Answer

To determine which of the given expressions are algebraic and which are arithmetic, we first need to understand the definitions of both types of expressions:

1. **Algebraic Expression**: An expression that contains at least one variable (like x, y, a, etc.) along with constants and arithmetic operations (addition, subtraction, multiplication, division).
2. **Arithmetic Expression**: An expression that contains only numbers and arithmetic operations, with no variables present.

Now, let's analyze each expression step by step:

### Step 1: Analyze Expression a: `22x - 11a`
- This expression contains the variables `x` and `a`.
- Since it has variables, it is classified as an **algebraic expression**.

### Step 2: Analyze Expression b: `6xnp`
- This expression contains the variables `x`, `n`, and `p`.
- Since it has variables, it is classified as an **algebraic expression**.

### Step 3: Analyze Expression c: `12 + (5 x 4) - 15`
- This expression contains only numbers (12, 5, 4, and 15) and arithmetic operations (addition and subtraction).
- Since there are no variables present, it is classified as an **arithmetic expression**.

### Step 4: Analyze Expression d: `5`
- This is a single numeric value with no variables.
- Since it contains only a number, it is classified as an **arithmetic expression**.

### Step 5: Analyze Expression e: `s`
- This expression contains the variable `s`.
- Since it has a variable, it is classified as an **algebraic expression**.

### Final Classification:
- a. `22x - 11a` → **Algebraic Expression**
- b. `6xnp` → **Algebraic Expression**
- c. `12 + (5 x 4) - 15` → **Arithmetic Expression**
- d. `5` → **Arithmetic Expression**
- e. `s` → **Algebraic Expression**

### Summary:
- Algebraic Expressions: a, b, e
- Arithmetic Expressions: c, d

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