We need to observe and analyze the given score to judge whether it is necessary to simplify it. If the numerator and denominator of a fraction are simple numbers or polynomials, then we can operate directly. If the numerator or denominator of a fraction is a complex expression, then we need to simplify it first to make the form of the fraction simpler and easier to calculate.
When simplifying, you can use some basic skills, such as simplification and divisibility. Simplification refers to dividing the numerator and denominator of a fraction by their common factors at the same time, thus making the form of a fraction simpler. General division refers to multiplying the numerator and denominator of a fraction by their common denominator at the same time, so that the value of the fraction remains unchanged, but the form is simpler.
In factorization, we can use some basic formulas and rules, such as extracting common factor, square difference formula, complete square formula and so on. By factorization, we can decompose a complex expression into several simple expressions, which makes it easier to calculate. When simplifying, we need to pay attention to some operational properties, such as commutative law, associative law and distributive law. These operational properties can help us simplify the calculation process and make the calculation easier without changing the value.
Matters needing attention in the evaluation of fractional simplification:
1. Determine the simplest form of the score: Before simplification, it is necessary to observe and analyze the form of a given score and determine its simplest form. In the process of simplification, we should try our best to avoid complicated calculation and derivation, so as not to increase the calculation difficulty and error.
2. Pay attention to the operation order and symbol: when simplifying the score, you need to pay attention to the change of operation order and symbol. Some fractions may need to be divided or divided many times, so be careful to avoid making mistakes. At the same time, we should pay attention to the sign change of the numerator or denominator in the fraction, and adjust the operation order and sign in time.
3. Pay attention to the accuracy when substituting numerical values: after obtaining the simplest form of the score, you need to substitute the given numerical value for calculation. When substituting numerical values, attention should be paid to the accuracy of numerical values and unit conversion. If there are decimals or fractions in the substitution value, it is necessary to ensure that the accuracy of decimals or fractions meets the requirements to avoid errors.