Answer :
Vamos a resolver cada una de las fracciones para encontrar el valor de [tex]\( x \)[/tex] de acuerdo con las ecuaciones proporcionadas en el crucigrama.
### HORIZONTALES
1. [tex]\(\frac{1}{x} = \frac{18}{36}\)[/tex]
Simplificamos la fracción a la derecha:
[tex]\[
\frac{18}{36} = \frac{1}{2}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{1}{x} = \frac{1}{2} \implies x = 2
\][/tex]
Por lo tanto, [tex]\( x = 2 \)[/tex] para esta ecuación.
2. [tex]\(\frac{2}{7} = \frac{72}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72 \cdot 7}{2} = 252
\][/tex]
Entonces, [tex]\( x = 252 \)[/tex].
### VERTICALES
3. [tex]\(\frac{x}{6} = \frac{17}{3} \quad \frac{7}{2}=\frac{x}{4}\)[/tex]
Primera parte:
[tex]\[
\frac{x}{6} = \frac{17}{3} \implies x = \frac{17 \cdot 6}{3} = 34
\][/tex]
Segunda parte:
[tex]\[
\frac{7}{2} = \frac{x}{4} \implies x = \frac{7 \cdot 4}{2} = 14
\][/tex]
1. [tex]\(\frac{2}{x}=\frac{12}{24}\)[/tex]
Simplificamos la fracción a la derecha:
[tex]\[
\frac{12}{24} = \frac{1}{2}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{2}{x} = \frac{1}{2} \implies x = 4
\][/tex]
6. [tex]\(\frac{x}{49} = \frac{64}{7}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{64 \cdot 49}{7} = 448
\][/tex]
4. [tex]\(\frac{63}{x} = \frac{6}{4} \quad \frac{x}{63} = \frac{2}{3}\)[/tex]
Primera parte:
[tex]\[
\frac{63}{x} = \frac{6}{4} \implies x = \frac{63 \cdot 4}{6} = 42
\][/tex]
Segunda parte:
[tex]\[
\frac{x}{63} = \frac{2}{3} \implies x = \frac{2 \cdot 63}{3} = 42
\][/tex]
2. [tex]\(\frac{2}{28}=\frac{23}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{23 \cdot 28}{2} = 322
\][/tex]
7. [tex]\(\frac{7}{x}=\frac{56}{16}\)[/tex]
Simplificamos la fracción a la derecha:
[tex]\[
\frac{56}{16} = \frac{7}{2}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{7}{x} = \frac{7}{2} \implies x = 2
\][/tex]
5. [tex]\(\frac{52}{14}=\frac{x}{7} \quad \frac{3}{x}=\frac{1}{6}\)[/tex]
Primera parte:
[tex]\[
\frac{52}{14} = \frac{x}{7} \implies x = \frac{52 \cdot 7}{14} = 26
\][/tex]
Segunda parte:
[tex]\[
\frac{3}{x} = \frac{1}{6} \implies x = 3 \cdot 6 = 18
\][/tex]
### Fracciones adicionales
1. [tex]\(\frac{3}{x}=\frac{1}{8}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 3 \cdot 8 = 24
\][/tex]
2. [tex]\(\frac{1}{9}=\frac{7}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 7 \cdot 9 = 63
\][/tex]
3. [tex]\(\frac{2}{15}=\frac{50}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{50 \cdot 15}{2} = 375
\][/tex]
4. [tex]\(\frac{5}{3}=\frac{x}{15}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5 \cdot 15}{3} = 25
\][/tex]
5. [tex]\(\frac{1}{15}=\frac{5}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 5 \cdot 15 = 75
\][/tex]
6. [tex]\(\frac{1}{x}=\frac{12}{60}\)[/tex]
Simplificamos esa fracción:
[tex]\[
\frac{12}{60} = \frac{1}{5}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{1}{x} = \frac{1}{5} \implies x = 5
\][/tex]
7. [tex]\(\frac{3}{x}=\frac{1}{7}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 3 \cdot 7 = 21
\][/tex]
8. [tex]\(\frac{45}{12}=\frac{x}{4}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{45 \cdot 4}{12} = 15
\][/tex]
### Soluciones
Los valores de [tex]\( x \)[/tex] para cada ecuación son:
```
(2.0, 252.0, 34.0, 14.0, 4.0, 448.0, 42.0, 42.0, 322.0, 2.0, 26.0, 18, 24, 63, 375.0, 45.0, 75, 5.0, 21, 15.0)
```
### HORIZONTALES
1. [tex]\(\frac{1}{x} = \frac{18}{36}\)[/tex]
Simplificamos la fracción a la derecha:
[tex]\[
\frac{18}{36} = \frac{1}{2}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{1}{x} = \frac{1}{2} \implies x = 2
\][/tex]
Por lo tanto, [tex]\( x = 2 \)[/tex] para esta ecuación.
2. [tex]\(\frac{2}{7} = \frac{72}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72 \cdot 7}{2} = 252
\][/tex]
Entonces, [tex]\( x = 252 \)[/tex].
### VERTICALES
3. [tex]\(\frac{x}{6} = \frac{17}{3} \quad \frac{7}{2}=\frac{x}{4}\)[/tex]
Primera parte:
[tex]\[
\frac{x}{6} = \frac{17}{3} \implies x = \frac{17 \cdot 6}{3} = 34
\][/tex]
Segunda parte:
[tex]\[
\frac{7}{2} = \frac{x}{4} \implies x = \frac{7 \cdot 4}{2} = 14
\][/tex]
1. [tex]\(\frac{2}{x}=\frac{12}{24}\)[/tex]
Simplificamos la fracción a la derecha:
[tex]\[
\frac{12}{24} = \frac{1}{2}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{2}{x} = \frac{1}{2} \implies x = 4
\][/tex]
6. [tex]\(\frac{x}{49} = \frac{64}{7}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{64 \cdot 49}{7} = 448
\][/tex]
4. [tex]\(\frac{63}{x} = \frac{6}{4} \quad \frac{x}{63} = \frac{2}{3}\)[/tex]
Primera parte:
[tex]\[
\frac{63}{x} = \frac{6}{4} \implies x = \frac{63 \cdot 4}{6} = 42
\][/tex]
Segunda parte:
[tex]\[
\frac{x}{63} = \frac{2}{3} \implies x = \frac{2 \cdot 63}{3} = 42
\][/tex]
2. [tex]\(\frac{2}{28}=\frac{23}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{23 \cdot 28}{2} = 322
\][/tex]
7. [tex]\(\frac{7}{x}=\frac{56}{16}\)[/tex]
Simplificamos la fracción a la derecha:
[tex]\[
\frac{56}{16} = \frac{7}{2}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{7}{x} = \frac{7}{2} \implies x = 2
\][/tex]
5. [tex]\(\frac{52}{14}=\frac{x}{7} \quad \frac{3}{x}=\frac{1}{6}\)[/tex]
Primera parte:
[tex]\[
\frac{52}{14} = \frac{x}{7} \implies x = \frac{52 \cdot 7}{14} = 26
\][/tex]
Segunda parte:
[tex]\[
\frac{3}{x} = \frac{1}{6} \implies x = 3 \cdot 6 = 18
\][/tex]
### Fracciones adicionales
1. [tex]\(\frac{3}{x}=\frac{1}{8}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 3 \cdot 8 = 24
\][/tex]
2. [tex]\(\frac{1}{9}=\frac{7}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 7 \cdot 9 = 63
\][/tex]
3. [tex]\(\frac{2}{15}=\frac{50}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{50 \cdot 15}{2} = 375
\][/tex]
4. [tex]\(\frac{5}{3}=\frac{x}{15}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5 \cdot 15}{3} = 25
\][/tex]
5. [tex]\(\frac{1}{15}=\frac{5}{x}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 5 \cdot 15 = 75
\][/tex]
6. [tex]\(\frac{1}{x}=\frac{12}{60}\)[/tex]
Simplificamos esa fracción:
[tex]\[
\frac{12}{60} = \frac{1}{5}
\][/tex]
Entonces, tenemos:
[tex]\[
\frac{1}{x} = \frac{1}{5} \implies x = 5
\][/tex]
7. [tex]\(\frac{3}{x}=\frac{1}{7}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = 3 \cdot 7 = 21
\][/tex]
8. [tex]\(\frac{45}{12}=\frac{x}{4}\)[/tex]
Despejamos [tex]\( x \)[/tex]:
[tex]\[
x = \frac{45 \cdot 4}{12} = 15
\][/tex]
### Soluciones
Los valores de [tex]\( x \)[/tex] para cada ecuación son:
```
(2.0, 252.0, 34.0, 14.0, 4.0, 448.0, 42.0, 42.0, 322.0, 2.0, 26.0, 18, 24, 63, 375.0, 45.0, 75, 5.0, 21, 15.0)
```
