Six theorems of proportion, combined ratio, divided ratio, combined ratio, multiple ratio, equal ratio and inverse ratio in junior high school mathematics;

Basic properties of proportion: if a: b = c: d, a× d = b× c.

Combinatorial theorem: if a: b = c: d, (a b): b = (c d)/d.

If a: b = c: d and there are b+a≠0 and d+c≠0, then a: (b+a) = c: (d+c).

If a: b = c: d and there are b-a≠0 and d-c≠0, then a: (b-a) = c: (d-c).

If a: b = c: d and there are b-na≠0 and d-nc≠0, then a: (b-na) = c: (d-NC).

Equal ratio theorem (equal ratio property): If A: B = C: D = M: N (B+D+…+N ≠ 0), (A+C+M): (B+D+N) = A: B.

theorem

Combinatorial theorem: if a/b=c/d, (a+b)/b=(c+d)/d(b, d≠0).

Fraction theorem: if a/b=c/d, (a-b)/b=(c-d)/d(b, d≠0).

Fraction theorem: If a/b=c/d, (a+b)/(a-b)=(c+d)/(c-d)(b, D, a-b, c-d≠0).

Equal ratio theorem: if a/b=c/d, a/c=b/d(a, b, c, d≠0).