Basic knowledge
Reduced points: Converts a fraction to be equal to it, but the numerator and denominator are relatively small, called reduced points.
Method of reduction: Use the common factor of the numerator and denominator (except 1) to remove the numerator and denominator of the fraction. Usually you have to divide until you get the simplest score.
The fraction whose numerator and denominator are relatively prime numbers is called the simplest fraction. The numerator and denominator of the simplest fraction have no common divisor other than 1. The simplest fraction is also called a reduced fraction. The reduced fraction can be understood as a fraction that has been reduced, that is, a fraction whose numerator and denominator are relatively prime numbers.
Solving method
For example, to find a simplest score so that its score value is greater than but less than. The solution method is as follows:
1. Passing multiples ratio
First pass the two scores, if after passing the scores, it is found that the numerators of the two scores only differ by 1 When it is time, it is necessary to expand it by a certain multiple (if it is the same denominator, it needs to be expanded directly, that is, expand the numerator and denominator by 2 times, 3 times, 4 times...) until the difference between the numerators is greater than 1.
That is;. The required score is.
2. Denominator comparison
Multiply the numerator and denominator of these two numbers by 2 at the same time (because multiplying by 2 is the simplest, if you multiply by other integers, you can), actually The above is to convert the original fraction into a fraction of the same numerator, then the fraction with a large denominator is small, and the fraction with a small denominator is large.
That is;. The required score is.
3. Find the average
It is to ask for the average of the sum of these two scores. It is analyzed based on the "if, then" arithmetic.
That is. The required score is.
4. Turn into decimals
First turn the fraction into decimals, then choose an appropriate decimal between these two decimals, and then rewrite it as a fraction.
That is. For example, take 0.18, and the required score is.
Teaching application
In the teaching of the simplest score, the standardization and rigor of the concept of the simplest score should be downplayed, and students’ individualized understanding and experience of the simplest score should be strengthened. You can start by creating a problem situation and let students go through the process of feeling, guessing, exemplifying, and understanding. In this process, students can make bold conjectures about the simplest score with their initial understanding and superficial feelings of the simplest score. As a result, the students' thoughts and thinking with obvious individuality can be exposed. The correctness of ideas is secondary. What is important is that students have the opportunity to express their true feelings and understanding of new knowledge. These ideas provide valuable resources for students to further abstract the essence of the simplest score. With the help of these one-sided, naive and even wrong ideas, the essential attributes of the simplest scores become clear from vagueness in the confrontation of ideas. This approach not only effectively mobilizes the enthusiasm of students in learning and transforms students' learning methods, but also pays full attention to the dynamic generation process of knowledge conclusions.
Example
Example 1. Simplify to the simplest fraction.
Solution:.
Example 2. Is it the simplest score?
Solution: 8 and 21 are relatively prime numbers, so they are the simplest fractions.