The simplest fraction is the moleculedenominatoronlyCommon factorFraction of 1, or numerator and denominatorCoprimeIs also called reduced fraction.For example, one half, two thirds, eight nineths, three eighths and so on.
ApproximationTo reduce a fraction to a fraction that is equal to it but has smaller numerator and denominator, it is called reduction.
Reduction method: remove the numerator and denominator of a fraction by using the common factor (except 1) of the numerator and denominator.It is usually divided until the minimum score is obtained.
A fraction whose numerator and denominator are coprime numbers is called the simplest fraction.The numerator and denominator of the simplest fraction have no other common divisor except 1.The simplest fraction is also called a reduced fraction, which can be understood as a reduced fraction, that is, a fraction whose numerator and denominator are coprime numbers.[1]
Solution method
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For example, to find a simplest fraction whose value is greater than
And less than
。The solution method is as follows:
1. Overall multiple ratio
The two fractions are first divided. If it is found that the numerator of the two fractions is only 1 difference after the general division, it is necessary to expand it by a certain number (if the denominator is the same, it is necessary to directly expand it, that is, the numerator and denominator are both expanded by 2 times, 3 times, 4 times...) until the difference between the numerators is more than 1.
I.e
；
。The score is
。
2. Denominator comparison
Multiply the numerator and denominator of these two numbers by 2 at the same time (because it is easiest to multiply by 2, and it can also be multiplied by other integers). In fact, the original
When a fraction is converted into a fraction with the same numerator, the fraction with a larger denominator is smaller, and the fraction with a smaller denominator is larger.
I.e
；
。The score is
。
3. Average
It is to ask for the average of the sum of these two scores, which is based on the "If
, then
”It is analyzed by calculation.
I.e
。The score is
。
4. Decimal
First convert the fraction into a decimal, then take an appropriate decimal between the two decimal, and then rewrite it into a fraction.
I.e
。For example, take 0.18,
, the score is
。[2]
Teaching application
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In the teaching of the simplest fraction, the standardization and preciseness of the concept of the simplest fraction should be weakened, and students' personalized understanding and experience of the simplest fraction should be strengthened.You can start from creating problem situations and let students go through the process of feeling, conjecture, illustration, perception, etc.In this process, students can rely on their initial understanding of the simplest score and surface feelings to make bold guesses about the simplest score.So that students' ideas and thinking with obvious personality color can be exposed.Whether the ideas are correct or not 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 fraction.Then, with the help of these one-sided, childish and even wrong ideas to start thinking and argumentation, in the ideological confrontation, the essential attribute of the simplest fraction has become clear from obscurity.This practice not only effectively mobilized the enthusiasm of students and changed their learning methods, but also fully focused on the dynamic generation process of knowledge conclusions.[3]
