Common methods of comparing the sizes of several numbers and their principles, from the questions, the median method, the reciprocal method,inequality (math.)The three methods of the method are examined more frequently.
Core knowledge
(1) Differential method
For any two numbers a, b.
If a - b ≥ 0, then a ≥ b; if a - b < 0, then a < b.
(2) Commercial law
When a and b are any two positive numbers, the
as
≥ 1, then a ≥ b; if
< 1, then a < b.
When a and b are any two negative numbers, the
as
≥ 1, then a ≤ b; if
< 1, then a > b.
(3) Intermediate value method
For any two numbers a and b, if an intermediate value c can be found that satisfies a > c and c > b, then a > b can be introduced.
(4) The inverse method
When a and b are of the same sign
as
≤
, then a ≥ b; if
＞
, then a < b.
(5) Inequality method (judgment based on the nature of inequality)
a. If a ≥ b, then a ± c ≥ b ± c;
If a ≥ b and c ≥ d, then a + c ≥ b + d and a - d ≥ b - c;
b. If a > b and c > 0, then ac > bc.
＞
；
If a > b and c < 0, then ac < bc.
＜
；
If a > b > 0 and c > d > 0, then ac > bd, and
＞
；
c. If a > b > 0, then an > bn (n > 1); if a > b > 0, then
＞
(n＞1)。
d, when an ≥ bn , n > 0 and n is even.
If a > 0 and b > 0, then a ≥ b > 0;
If a < 0 and b < 0, then a ≤ b < 0.
When an ≥ bn , n > 0 and n is odd, then a ≥ b.
(6) Difference-in-differences comparison method
In general, when comparing the sizes of several fractions, if their values are close to "1" or some integer, then
These fractions can be compared by comparing their difference from "1".