REX05 Reducing Rational Expressions to Lowest Terms Part 1

In the previous video, we have learned about domain of rational functions. In this video, we are going to learn about how to reduce rational expressions particularly fractions to lowest terms.  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

Reduce the following to lowest terms.

1.) \dfrac{8}{12}

2.) \dfrac{15}{25}.

3.) \dfrac{9}{27}.

4.) \dfrac{6}{24}.

5.) $latex  \dfrac{10}{22}$.

Answers

1.) \dfrac{2}{3}

2.) \dfrac{3}{5}.

3.) \dfrac{1}{3}.

4.) \dfrac{1}{4}.

5.) $latex  \dfrac{5}{11}$.
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REX01 Introduction to Rational Expressions

In this video, we learn the definition of rational numbers, rational expressions, and rational functions .  Watch the Tagalog math tutorial video above and then answer the exercises below. The complete video playlist of the Sipnayan tutorials on Rational Expressions can be found here.

Practice Exercise

True or False

1.)  The fraction \frac{\pi}{3} is a rational number.

2.) The fraction \frac{2x - 1}{5x + 1} is a rational expression.

3.) The fraction \frac{\sqrt{x} + 3}{x^2 + 3} is a rational expression.

4.) The function f(x) = \frac{1}{x} is a rational function.

5.) The fraction \frac{3}{8} is a rational number.

Answers

1.False. The numerator and denominator of a rational number must be integers.
2. True
3. False. \sqrt{x} + 3 is not a polynomial expression.
4. True
5. True

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Lahat ba ng fractions ay rational numbers?

Hindi. Halimbawa, ang \frac {\pi}{3} ay fraction pero hindi ito rational number.

Gaya na nagpagaralan natin, ang rational numbers ay ang mga numerong pwedeng i-express na ratio ng dalawang integers. Dahil ang \pi ay irrational, hindi natin ito pwedeng i-express bilang integer o ratio ng integers. Ito ang dahilan kung kaya kahit fraction ang \frac{\pi}{3} ay hindi ito rational number.

Malamang ay nahalata ninyo na kapag ang numerator ng fraction ay irrational at ang denominator ay rational (o vice versa), automatic na na irrational ang fraction na ito. Kaya, ang fractions na

\displaystyle\frac{\sqrt{2}}{2}, \displaystyle\frac{3}{e} at \displaystyle\frac{2 }{3 \pi}

ay irrational numbers.

Introduction to Rational Numbers

Napagusapan na natin ang irrational numbers kaya sa post na ito,  pag-uusapan naman natin ang rational numbers.  Ang rational numbers ay mga numero na pwedeng i-express as fractions. Sa formal definition, ito ay mga numero na pwedeng isulat sa form na \frac{a}{b}, kung saan ang a at b ay integers at b \neq 0 (ang symbol na \neq ay nangangahulugang “not equal”). Sa ganitong form, kita natin na ang lahat ng integers ay rational numbers din. Ito ay dahil pwede tayong maglagay na denominator na 1 sa lahat ng integers positive man o negative.

Halimbawa,

-3 = \frac{-3}{1} = \frac{a}{b}

kung saana = 3 at b = 1. Siyempre, ang zero ay rational number din dahil 0 = \frac{0}{1}.

Rational numbers din ang terminating decimals, at rational numbers din ang non-terminating repeating decimals. Paguusapan natin ito sa hiwalay na post.

Ang rational numbers at irrational numbers kapag pinagsama ang bumubuo sa real numbers.  Ito ay ipinapakita sa diagram sa itaas. Makikita natin na ang integers, whole numbers, at natural numbers ay subsets  ng rational numbers. Tingnang mabuti ang diagram dahil may iilang maling representation ng real number system sa ilang websites.

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