Algebraic fraction multiplication

THE algebraic fraction has at least one unknown (unknown number represented by a letter) in the denominator. This unknown is what differentiates them from monomials, that are algebraic expressions who have a multiplication from known numbers to unknown numbers. Thus, algebraic fractions are representations of multiplication and division operations between numbers and unknowns and, therefore, obey the same properties and rules of operations between numbers real.

Algebraic fraction multiplication

At algebraic fractions they are multiplied just like numeric fractions. The two differences are:

• In the algebraic fractions, it is not necessary multiply the unknowns, just rewrite them together, keeping, of course, the potency properties;

• It is necessary to use the potency properties and polynomial factorization to solve some problems.

For example:

4x³y⁴·18x²k²y²
9kh 2x⁴y⁵

multiply the fractions above gives the following result:

4x³y⁴18x²k²y²
9kh2x⁴y⁵

By rearranging the factors, we can find:

18·4x²x³y⁴y²k²
2·9x⁴y⁵kh

Now just do the multiplications numerical values ​​and use the properties of the powers to simplify the result. The first property is that of multiplication: in the product of powers of the same base, the base is preserved and the exponents are added.

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72x²⁺³y⁴⁺²k²
18x⁴y⁵kh

72x⁵y⁶k²
18x⁴y⁵kh

We can simplify the algebraic fraction with the property of power division. In the division of powers of the same base, the base is conserved and the exponents are subtracted. If it is possible to simplify the numerical fraction, simplify it.

72x⁵y⁶k²
18x⁴y⁵kh

4x^5-4y^6-5k^2-1
H

4x¹y¹k¹
H

This is the final result of the multiplication between the algebraic fractions from the example. It is possible to omit exponent 1, making the result:

4xyk
H

A multiplication of algebraic fraction can give rise to several cases of simplification. These cases can be obtained on here. To facilitate this simplification, it is important that the student knows the notable products of polynomials and the multiplication properties.

By Luiz Paulo Moreira
Graduated in Mathematics

Would you like to reference this text in a school or academic work? Look:

SILVA, Luiz Paulo Moreira. "Algebraic fraction multiplication"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/multiplicacao-fracao-algebrica.htm. Accessed on June 28, 2021.

Polynomial

Learn the definition of polynomial equation, define a polynomial function, the numerical value of a polynomial, the root or zero of the polynomial, Degree of a polynomial.