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Answer :
Sure! Let's go through the process of simplifying the fractions and finding equivalent fractions step-by-step.
### Part 1: Simplifying the Fractions
a) [tex]\(\frac{3}{6}\)[/tex]
- To simplify [tex]\(\frac{3}{6}\)[/tex], find the greatest common divisor (GCD) of 3 and 6, which is 3.
- Divide both the numerator and the denominator by 3.
- [tex]\(\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}\)[/tex]
b) [tex]\(\frac{8}{12}\)[/tex]
- Find the GCD of 8 and 12, which is 4.
- Divide both the numerator and the denominator by 4.
- [tex]\(\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)[/tex]
c) [tex]\(\frac{2}{4}\)[/tex]
- Find the GCD of 2 and 4, which is 2.
- Divide both the numerator and the denominator by 2.
- [tex]\(\frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2}\)[/tex]
### Part 2: Finding Equivalent Fractions
a) [tex]\(\frac{24}{30}\)[/tex]
- Find the GCD of 24 and 30, which is 6.
- The simplified form: [tex]\(\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex]
- Two equivalent fractions:
- Multiply the simplified fraction by 2: [tex]\(\frac{8}{10}\)[/tex]
- Multiply the simplified fraction by another factor (for example, 3): [tex]\(\frac{12}{15}\)[/tex]
b) [tex]\(\frac{18}{24}\)[/tex]
- Find the GCD of 18 and 24, which is 6.
- The simplified form: [tex]\(\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}\)[/tex]
- Two equivalent fractions:
- Multiply the simplified fraction by 2: [tex]\(\frac{6}{8}\)[/tex]
- Multiply the simplified fraction by another factor (for example, 3): [tex]\(\frac{9}{12}\)[/tex]
c) 36 as a fraction over 1 is [tex]\(\frac{36}{1}\)[/tex]
- The simplest form of 36 is already [tex]\(\frac{36}{1}\)[/tex].
- Two equivalent fractions:
- Multiply by 2: [tex]\(\frac{72}{2}\)[/tex]
- Multiply by 3: [tex]\(\frac{108}{3}\)[/tex]
By following these steps, you've simplified the fractions and found two equivalent fractions for each. If you need any further clarification or help, feel free to ask!
### Part 1: Simplifying the Fractions
a) [tex]\(\frac{3}{6}\)[/tex]
- To simplify [tex]\(\frac{3}{6}\)[/tex], find the greatest common divisor (GCD) of 3 and 6, which is 3.
- Divide both the numerator and the denominator by 3.
- [tex]\(\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}\)[/tex]
b) [tex]\(\frac{8}{12}\)[/tex]
- Find the GCD of 8 and 12, which is 4.
- Divide both the numerator and the denominator by 4.
- [tex]\(\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)[/tex]
c) [tex]\(\frac{2}{4}\)[/tex]
- Find the GCD of 2 and 4, which is 2.
- Divide both the numerator and the denominator by 2.
- [tex]\(\frac{2}{4} = \frac{2 \div 2}{4 \div 2} = \frac{1}{2}\)[/tex]
### Part 2: Finding Equivalent Fractions
a) [tex]\(\frac{24}{30}\)[/tex]
- Find the GCD of 24 and 30, which is 6.
- The simplified form: [tex]\(\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex]
- Two equivalent fractions:
- Multiply the simplified fraction by 2: [tex]\(\frac{8}{10}\)[/tex]
- Multiply the simplified fraction by another factor (for example, 3): [tex]\(\frac{12}{15}\)[/tex]
b) [tex]\(\frac{18}{24}\)[/tex]
- Find the GCD of 18 and 24, which is 6.
- The simplified form: [tex]\(\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}\)[/tex]
- Two equivalent fractions:
- Multiply the simplified fraction by 2: [tex]\(\frac{6}{8}\)[/tex]
- Multiply the simplified fraction by another factor (for example, 3): [tex]\(\frac{9}{12}\)[/tex]
c) 36 as a fraction over 1 is [tex]\(\frac{36}{1}\)[/tex]
- The simplest form of 36 is already [tex]\(\frac{36}{1}\)[/tex].
- Two equivalent fractions:
- Multiply by 2: [tex]\(\frac{72}{2}\)[/tex]
- Multiply by 3: [tex]\(\frac{108}{3}\)[/tex]
By following these steps, you've simplified the fractions and found two equivalent fractions for each. If you need any further clarification or help, feel free to ask!
Thanks for taking the time to read 1 Simplifica las fracciones al máximo y represéntalas gráficamente a tex frac 3 6 tex tex square tex b tex frac 8 12 tex tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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Simplifica las fracciones al máximo y represéntalas gráficamente:
a) [tex]\frac{3}{6}[/tex]
Para simplificar [tex]\frac{3}{6}[/tex], buscamos el máximo común divisor (MCD) de 3 y 6, que es 3. Dividimos ambos numerador y denominador entre 3:
[tex]\frac{3 \div 3}{6 \div 3} = \frac{1}{2}[/tex]
La fracción simplificada es [tex]\frac{1}{2}[/tex].- Gráficamente: Representamos esta fracción como un círculo dividido en 2 partes iguales, con 1 parte coloreada.
b) [tex]\frac{8}{12}[/tex]
El MCD de 8 y 12 es 4. Dividimos:
[tex]\frac{8 \div 4}{12 \div 4} = \frac{2}{3}[/tex]
La fracción simplificada es [tex]\frac{2}{3}[/tex].- Gráficamente: Un círculo dividido en 3 partes iguales, con 2 partes coloreadas.
c) [tex]\frac{2}{4}[/tex]
El MCD de 2 y 4 es 2. Por lo tanto:
[tex]\frac{2 \div 2}{4 \div 2} = \frac{1}{2}[/tex]
La fracción simplificada es [tex]\frac{1}{2}[/tex].- Gráficamente: Igual que la primera, un círculo dividido en 2 partes iguales, con 1 parte coloreada.
Simplifica cada fracción para obtener dos fracciones equivalentes:
a) [tex]\frac{24}{30}[/tex]
El MCD de 24 y 30 es 6. Dividimos:
[tex]\frac{24 \div 6}{30 \div 6} = \frac{4}{5}[/tex]- Fracciones equivalentes: [tex]\frac{48}{60}[/tex] y [tex]\frac{12}{15}[/tex].
b) [tex]\frac{18}{24}[/tex]
El MCD de 18 y 24 es 6. Dividimos:
[tex]\frac{18 \div 6}{24 \div 6} = \frac{3}{4}[/tex]- Fracciones equivalentes: [tex]\frac{9}{12}[/tex] y [tex]\frac{6}{8}[/tex].
c) [tex]\frac{36}{\square}[/tex]
Necesitamos conocer el denominador para simplificar y obtener equivalentes. Por ejemplo, si [tex]\square = 48[/tex]:
El MCD de 36 y 48 es 12. Así que:
[tex]\frac{36 \div 12}{48 \div 12} = \frac{3}{4}[/tex]- Fracciones equivalentes: [tex]\frac{9}{12}[/tex] y [tex]\frac{6}{8}[/tex].
Espero que esta explicación te ayude a entender cómo simplificar y encontrar fracciones equivalentes. ¡Si tienes más dudas, no dudes en preguntar!
