Here are some of the most important equations in elementary **mathematics**:

1. Addition: a + b = c

For example, 2 + 3 = 5

2. Subtraction: a – b = c

For example, 8 – 4 = 4

3. Multiplication: a x b = c

For example, 5 x 6 = 30

4. Division: a / b = c

For example, 18 / 6 = 3

5. **Pythagorean** theorem: a² + b² = c²

Used to find the length of the hypotenuse in a right triangle.

6. Area of rectangle: A = l x w

Used to find the area of a rectangle, where l is the length and w is the width.

7. Area of triangle: A = 1/2 x b x h

Used to find the area of a triangle, where b is the base and h is the height.

8. Order of operations:

Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

These equations are essential to understand and apply in many areas of mathematics and in everyday life.