Ratio and Proportions:

Ratio and proportions are the foundational concepts of mathematics. A ratio is a comparison of two numbers that shows how much one value is greater or smaller than the other. It is represented in the form of a fraction, and it can be simplified.

Solution:

Let's assume the number we are looking for be x. Then, according to the problem statement, we can set up the following proportion:

6/13 = x/26

We can solve for x by cross-multiplying:

6(26) = 13x

156 = 13x

x = 156/13

x = 12

Therefore, the required number is 12.

Explanation:

The problem statement states that there is a certain number, let's call it x, which has the same ratio to 26 as 6 has to 13. This means that the ratio of 6 to 13 is the same as the ratio of x to 26. In other words, the two ratios are proportional.

We can set up a proportion using these ratios, as shown above. To solve for x, we cross-multiply the fractions. This means that we multiply the numerator of one fraction with the denominator of the other fraction, and vice versa.

After cross-multiplying, we get an equation with x on one side. We can solve for x by dividing both sides of the equation by 13. This gives us the value of x, which is 12.

Therefore, the number which has the same ratio to 26 that 6 has to 13 is 12.