How to reduce a fraction without the help of a calculator

The world of high technologies predisposes people to work less. For this reason, fast food services have gained immense popularity, even despite obvious harm to such food for the body. The accessibility of the Internet has made the learning process different from what it was before. Now, to solve a complex problem, just go to the popular search engine and enter part of the job in the search box. As a result of this technogenic breakthrough, the whole society begins to gradually degrade.

Many today can not independently explain to their children how to reduce the fraction, especially if it does not concern elementary operations with numbers. I'm not talking about trigonometric formulas and actions. We ourselves will not have to sit for five minutes to remember what happened at school. And it's not a fact that we can intelligibly explain what we can remember.

Incorrect fractions and their transformation

A fraction in which the numerator is larger than the denominator is called incorrect. In order to isolate the whole component, it is necessary to divide the upper part of the fraction into a lower one. Separate from the division, write separately, and put the remainder in the numerator. The denominator of the fraction remains unchanged.

Fractions with variables

In the case when both the numerator and the denominator of the fraction contain a letter, its reduction occurs as follows:

1. If the letters are different, then you can go to the reduction of numbers:

2a / 4c = a / 2c

2. If the variables are the same:

3ac / 7cc = 3a / 7x

3. In the case when the numbers are in degree, then for the same bases, the reduction of the fraction occurs by subtracting from a larger degree less:

3 ^{7/3 12} = 3 ^{0/3 12-7} = ^{1/3 5}

4. Such actions are carried out in cases where the degree is present in a variable:

And ¹² to ³ / a ¹⁰ to ⁵ = a ^12-10 / to ^5-3 = a ² / to ²

In the case where the bases are different, it is not possible to reduce the fractions.

Fractions containing expressions

How to reduce fractions, the numerator of which consists of the sum or difference? In this case, it is necessary to apply the formulas of reduced multiplication or to expand the expression into multipliers. It is worth remembering, when the sum is in the numerators, then it can be reduced only in case of complete coincidence with the denominator:

(A + k) / (a + k) ² = 1 / (a + k) and (a + k) / a = ak + k / k = ak + 1

For example, how to reduce a fraction of the following type:

(4k ² + 4cr + p ² ) / (2k + p)

To perform the reduction, use the inverse square formula of the sum in the numerator and get:

4k ² + 4kr + p ² = (2k + p) ²

Now, when the numerator and denominator coincide, we have nothing left to do but to reduce the fraction:

(2k + p) ² / (2k + p) = (2k + p) / 1 = 2k + p

In order to easily reduce fractions, it is necessary to know and skillfully apply the formulas of reduced multiplication. For many, this seems a serious problem, but with their frequent use, they are perfectly remembered. It develops the human brain, teaches him to see the solution of intricate problems.

A wonderful approach to how to reduce the fraction, and its diversity. This allows you to give free rein to the creative component together with the intellectual. If we force our children to solve such examples on their own, then we can help them adapt faster to the changing and unexpected turns of life.