If A and B represent two algebraic expressions and B contains letters, then the formula A/B is called a fraction.

The numerator of a fraction is multiplied by the denominator or divided by an algebraic expression that is not equal to 0, and the value of the fraction remains the same.

Law of fractional multiplication: fractional multiplication, the product of molecules is the numerator of the product, and the product of denominator is the denominator.

Law of fractional division: a fraction is divided by a fraction, and the numerator and denominator of the divisor are in turn multiplied by the divisor.

Fractional power should be numerator and denominator respectively.

a^-n= 1/a^n？ (a≠0)？ So a-n? (a≠0) is the reciprocal of n.

Test method of fractional equation: bring the solution of the whole equation into the simplest common denominator. If the value of the simplest common denominator is not 0, the solution of the whole equation is the solution of the original fractional equation; Otherwise, this solution is not the solution of the original fractional equation.

Chapter 17 Inverse proportional function

A function in the form of y = k/x (where k is a constant and k≠0) is called an inverse proportional function.

The image of inverse proportional function belongs to hyperbola.

When k > 0, the two branches of hyperbola are located in the first quadrant and the third quadrant respectively, and the y value of each quadrant decreases with the increase of x value;

When k < 0, the two branches of hyperbola are located in the second quadrant and the fourth quadrant respectively, and the y value of each quadrant increases with the increase of x value.

Chapter 18 Pythagorean Theorem

Pythagorean Theorem: If the lengths of two right-angled sides of a right-angled triangle are A and B respectively and the length of the hypotenuse is C, then A 2+B 2 = C 2.

Inverse Theorem of Pythagorean Theorem: If the lengths of three sides of triangle A, B and C satisfy A 2+B 2 = C 2, then the triangle is a right triangle.

A proposition that is proved to be correct is called a theorem.

We call two propositions with opposite topics and conclusions reciprocal propositions. If one of them is called the original proposition, then the other is called its inverse proposition. (Example: Pythagorean Theorem and Pythagorean Theorem Inverse Theorem)

Chapter 19 Quadrilateral

A quadrilateral with two sets of parallel opposite sides is called a parallelogram.

The nature of parallelogram: the opposite sides of parallelogram are equal; Diagonal angles of parallelogram are equal. Diagonal bisection of parallelogram.

Determination of parallelogram;

1. Two groups of quadrangles with equal opposite sides are parallelograms;

2. The quadrilateral whose diagonal lines bisect each other is a parallelogram;

3. Two groups of quadrangles with equal diagonal are parallelograms;

4. A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

The midline of the triangle is parallel to the third side of the triangle and equal to half of the third side.

The center line of the hypotenuse of a right triangle is equal to half of the hypotenuse.

The nature of the rectangle: all four corners of the rectangle are right angles; The diagonals of a rectangle are equally divided. ?

Rectangular judgment theorem;

1. A parallelogram with a right angle is called a rectangle.

2. Parallelograms with equal diagonals are rectangles.

A quadrilateral with three right angles is a rectangle.

The nature of the diamond: all four sides of the diamond are equal; The two diagonals of the diamond are perpendicular to each other, and each diagonal bisects a set of diagonals. ?