How to reduce the fraction? Rules for all situations
Without knowledge of how to reduce a fraction, and the availability of a stable skill in solving such examples, it is very difficult to learn algebra in school. The further, the more on the basic knowledge of the reduction of ordinary fractions superimposed new information. Degrees appear first, then multipliers, which later become polynomials.
How can you not get confused? Fundamentally reinforce skills in previous topics and gradually prepare for knowledge on how to reduce fractions, which are becoming more complex from year to year.
Without them you can not cope with the tasks of any level. To understand how to reduce the fraction, you need to clarify two simple points. First: you can reduce only the multipliers. This nuance is very important when polynomials appear in the numerator or denominator. Then you need to clearly distinguish where the multiplier is, and where the term is.
The second point suggests that any number can be represented as multipliers.Moreover, the result of the reduction is such a fraction, the numerator and denominator of which can no longer be reduced.
Rules for reducing ordinary fractions
For a start it is worth checking whether the numerator is divisible by denominator or vice versa. Then it is on this number you need to make a reduction. This is the easiest option.
The second is the analysis of the appearance of numbers. If both end in one or more zeros, then they can be reduced by 10, 100 or a thousand. Here you can see whether the numbers are even. If so, then you can safely cut by two.
The third rule of how to reduce the fraction becomes the decomposition into prime factors of the numerator and denominator. At this time, you need to actively use all the knowledge about the signs of divisibility of numbers. After such a decomposition it remains only to find all the duplicates, multiply them and make a reduction by the resulting number.
What if the fraction is an algebraic expression?
Here are the first difficulties. Because it is here that the terms appear that may be identical to the multipliers. They really want to cut, but not. Before reducing the algebraic fraction, it must be transformed so that it has multipliers.
This will require several steps.You may need to go through them all, and maybe the first one will give the appropriate option.
Check whether the numerator and the denominator or any expression in them differ by sign. In this case, you just need to factor out the minus one. So get the same factors that can be reduced.
See if the common factor can be taken out of the polynomial by the brackets. Perhaps this will result in a bracket, which can also be shortened, or it will be a rendered monomial.
Try to group the monomials in order to later make a common factor in them. After that, it may turn out that multipliers appear that can be reduced, or the general elements can be repeated again.
Try to consider the abbreviated multiplication formulas in the notation. With their help, it is easy to convert a polynomial into factors.
The sequence of actions with fractions with degrees
In order to easily understand the question of how to reduce a fraction with degrees, it is necessary to firmly remember the basic actions with them. The first of these is related to the multiplication of powers. In this case, if the bases are the same, the indicators must be added up.
The second is the division.Again, for those that have the same basis, indicators will need to be subtracted. And you need to subtract from the number that stands in the dividend, and not vice versa.
The third is the raising to the degree of degree. In this situation, the indicators are multiplied.
Successful reduction will also require the ability to bring degrees to the same grounds. That is to see that four is two in a square. Or 27 - a cube of three. Because it is difficult to cut 9 in a square and 3 in a cube. But if you convert the first expression to (32)2, the reduction will be successful.