Answer :
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!
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!
