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a. Hallar la relación entre las edades de dos niños 12 y 18 años. b. Cite tres pares de números que están en la misma relación.

Let's start with part a:

To find the relationship between the ages of two children who are 12 and 18 years old, we can express this as a ratio. The ratio of their ages is:

$\frac{12}{18} = \frac{2}{3}$

Thus, the relationship between the ages of the two children is $2:3$. This means for every 2 years the younger child has, the older child has 3 years.

Now, for part b, you need to cite three pairs of numbers that have the same ratio, $2:3$. Some examples include:

1. $(4, 6)$ because $\frac{4}{6} = \frac{2}{3}$
2. $(6, 9)$ because $\frac{6}{9} = \frac{2}{3}$
3. $(8, 12)$ because $\frac{8}{12} = \frac{2}{3}$

Would you like any further explanations or details?

Five Related Questions:

1. How do you simplify a ratio like $\frac{12}{18}$ step by step?
2. Can a ratio be used to compare quantities other than ages?
3. How can you find more pairs of numbers in the same ratio $2:3$?
4. What is the difference between a ratio and a proportion?
5. How can you represent this ratio graphically?

Tip:

When simplifying ratios, divide both terms by their greatest common divisor (GCD). For $12$ and $18$, the GCD is 6, so you get $2:3$.