## AI Basic Arithmetic Solver

AI Basic Arithmetic Solver is designed to solve basic arithmetic problems. MathCrave AI-powered can interpret mathematical expressions and equations, utilizing algorithms and computational methods to provide accurate solutions. It can handle various arithmetic operations such as addition, subtraction, multiplication, and division, helping users solve math problems quickly and efficiently.

### Basic Arithmetic in Basic Algebra

Basic arithmetic in algebra involves operations such as addition, subtraction, multiplication, and division of algebraic expressions. Understanding these fundamental operations is essential for solving more complex algebraic equations and problems.

#### Basic Operations

1. Addition: Combining like terms.

2. Subtraction: Removing like terms.

3. Multiplication: Using the distributive property.

4. Division: Dividing coefficients and managing powers of variables.

#### Worked Examples

**1. Addition of Like Terms:**

\[

3x + 5x = (3 + 5)x = 8x

\]

Guide: Combine the coefficients of \(x\).

**2. Subtraction of Like Terms:**

\[

7y – 2y = (7 – 2)y = 5y

\]

Guide: Subtract the coefficients of \(y\).

**3. Addition of Unlike Terms:**

\[

3x + 4y = 3x + 4y

\]

Explanation: \(x\) and \(y\) are different terms and cannot be combined.

**4. Subtraction of Unlike Terms:**

\[

5a – 3b = 5a – 3b

\]

Guide: \(a\) and \(b\) are different terms and cannot be combined.

**5. Multiplication of a Constant and a Variable:**

\[

4 \cdot 3x = 12x

\]

Guide: Multiply the constant by the coefficient of \(x\).

**6. Multiplication of Variables:**

\[

2x \cdot 3x = (2 \cdot 3) x^2 = 6x^2

\]

Guide: Multiply the coefficients and add the exponents of \(x\).

**7. Multiplication Using the Distributive Property:**

\[

2x(3x + 4) = 2x \cdot 3x + 2x \cdot 4 = 6x^2 + 8x

\]

Guide: Distribute \(2x\) to each term inside the parentheses.

**8. Division of a Constant and a Variable:**

\[

\frac{12x}{4} = 3x

\]

Guide: Divide the coefficient by the constant.

**9. Division of Variables:**

\[

\frac{15x^3}{5x} = \frac{15}{5} \cdot \frac{x^3}{x} = 3x^{3-1} = 3x^2

\]

Guide: Divide the coefficients and subtract the exponents of \(x\).

**10. Combining Operations:**

\[

2x^2 + 3x – 5x + 4 = 2x^2 + (3x – 5x) + 4 = 2x^2 – 2x + 4

\]

Explanation: Combine like terms, \(3x\) and \(-5x\).

#### Analytical Explanation

In algebra, handling basic arithmetic operations correctly is crucial for simplifying and solving equations. Each operation follows specific rules:

– Addition and Subtraction: Only like terms (terms with the same variable and exponent) can be combined.

– Multiplication: Use the distributive property and apply the rules of exponents (i.e., \(x^a \cdot x^b = x^{a+b}\)).

– Division: Divide coefficients and subtract exponents (i.e., \(\frac{x^a}{x^b} = x^{a-b}\)).