1. Fractional proportional divisibility: If a: b = m: n (m and n are coprime), then a is a multiple of m and b is a multiple of n. ..

If a=m/n×b, then a=m/(m+n)×(a+b), that is, a+b is a multiple of m+n.

2. The mantissa method (1) has different mantissas, and the algorithm is addition, subtraction, multiplication and power operation, so the mantissa is preferred in judgment;

(2) There are a lot of calculation data, and mantissa judgment should be considered when the calculation is complicated to get the answer quickly. Often used for inclusion and exclusion principles.

3. arithmetic progression correlation formula: sum = (first item+last item) × number of items ÷2= average × number of items = median × number of items;

Project number = (last project-first project) ÷ Project number+1. Starting from 1, n consecutive odd numbers are added, and the sum is =n×n, such as 1+3+5+7=4×4= 16. ...

4. Geometric edge problem related formula: (1) unilateral linear tree planting formula (planting trees at both ends): tree = total length ÷ interval+1, total length = (tree-1)× interval.