In the first line, we have five divisions in the number line. If we need to represent the fraction 2/5, we need to count two divisions ahead (from zero) to find the point in the graph that represents 2/5. That is:
In the other number line, we have ten divisions. We know that if we multiply the numerator and the denominator of a fraction by the same number, we have another fraction, which means that the fraction has the same ratio (the same value), that is, this is an equivalent fraction.
We can see that as follows:
We multiply the original fraction 2/5 by 2/2, and we got 4/10, which is an equivalent fraction when the denominator is 10. If we simplify the fraction, we obtain again the fraction 2/5.
In summary, in the first case, we need to count 2 divisions to obtain the fraction 2/5, and, in the second case, having that the equivalent fraction is 4/10, we need to move the dot to 4/10 as is shown above.
