The fractions referred to in this paper are not fractions that reflect various test scores or assessment criteria, but are mathematical calculations consisting of numerators, denominators, and fraction lines. I hope to use fractions as a form of mathematics to rationally analyze and understand the importance of achieving healing and full recovery from mental illness. Many patients and their families are pessimistic when they suffer from mental illness. 1. Because they do not know the knowledge of mental illness regression and the possibilities and methods to achieve the best regression. 2. The helplessness and often pessimistic cognitive habits in the face of the patient’s post-onset disease manifestations make it difficult for them to look forward to a prospect that may not be pessimistic. 3, The general population’s automatic habit of accepting pessimistic, crowd-sourced rumors about mental illness. 4. There may also be the last straw that breaks the camel’s back – social discrimination against people with mental illness and the stigma of illness among patients and their families. How can patients with mental illness and their relatives be made to view and cope with the predicament of having a mental illness in a correct and even relatively optimistic manner? I think that in addition to the medical behavior based on high medical ethics and kindness, i.e., using the right professional knowledge and technology to correctly diagnose and treat the illness, and using the best rehabilitation treatment concept and technology to facilitate the patient’s functional recovery and return to society, medical professionals should also help them learn to use the big picture concept of “looking at the big picture”. We should also help them learn to correctly assess the general direction of the disease and realize that the disease is only a section of the river of life that is mixed with tributaries containing bitter water, but not the whole river of life. In my daily work, I use two fractional values to explain such understanding and philosophy to patients and their families. 1. Calculate the ratio of the length of illness to the length of life. I say, under the premise of active and effective treatment of the disease, the length of time after the disease to cure as the numerator, the length of human life as the denominator, the fraction must be a very small fraction of the value of the fraction: Suppose a juvenile bipolar disorder patients who started the disease at the age of 15 began treatment after one year of illness, if the treatment is effective, good recovery, it takes 3-5 years to reach the level of cure. Including the year before treatment, the time from illness to cure is 4-6 years. If we take the average life expectancy of local residents in Guangzhou as 81.34 years (2015 statistics), with 4-6 years as the numerator and the average life expectancy of 80 years as the denominator, this fraction value is between one-twentieth and three-fortieths. With such a calculation process, both the patients themselves and their families will realize that the duration of the patient’s illness can be a minuscule fraction. In this way, their willingness and confidence in treating the disease will be greatly enhanced. Even for patients with longer disease duration, if they can adhere to the standard treatment, the ratio or fraction of the length of time they are in painful suffering from the disease due to their illness to the length of their life is a small or insignificant value. Many patients and their families do not think this way after the disease, because they are accustomed to the negative cognitive model of “always taking the present as forever”. 2. Calculate the ratio of the length of treatment to the length of life. In the eyes of many patients and their families, the relative long-term nature of medication for mental illness, which is mostly a chronic process, also makes them feel that treatment is a distant journey. In fact, modern psychiatry has shown psychiatrists and patients an increasingly bright future: under the premise of correct diagnosis, after systematic and standardized specialized treatment including psychotherapy and solid and effective rehabilitation training, most patients are likely to achieve a cure after their first or even second episode, and most of them are more likely to fully recover their social functions and return to society. The majority of these patients are more likely to fully recover their social functions, return to society, and become normal members of society. What is even more encouraging is that if these patients maintain their social functions and play their social roles well enough in a normal social environment for a long time, their psychological quality improves, and their psychological maturity develops to the standard of their healthy peers, i.e., they reach the standard of complete cure, the risk of relapse after stopping medication is very low. At this point, these people are no different from healthy people and are fully equipped to enjoy a happy life without medication. Of course, there are many factors that influence the length of time it takes to reach this standard, and the most important ones that have the potential to shorten this time are at least two of the following 1. from a variety of effective therapeutic interventions implemented mainly by professionals 2. The patient’s persistent efforts: both the consistent acceptance of standardized treatment and rehabilitation, and the consistent pursuit and implementation of the goal of restoring social function and promoting psychological growth. The latter is even more important for achieving a final outcome that allows for full recovery. According to the general principles of developmental psychology and psychiatry, if a bipolar disorder patient who started at the age of 15 and began standardized treatment at the age of 16, for example, reaches the standard of full recovery after a maximum of 10 years of treatment, the patient will be only 26 years old and can become a normal member of society who can earn a living, fall in love, get married, and have children. Taking the treatment period of up to 10 years as the numerator and the life expectancy of 80 years as the denominator, this fraction is also only one eighth. If we use the standardized treatment and rehabilitation of one-eighth of the length of life to win the happiness of the second fifty years of life, it is very cost-effective in any way. I believe that if patients and their families have carefully calculated the above two fractional values and pursued the goal of complete cure on this basis, having a mental illness is not a big deal.