Third Proportional Explained

To find the third proportional to two given numbers, let's call them a and b, we are looking for a third number, let's call it c, such that the ratio of the first number to the second number is equal to the ratio of the second number to the third number. This means a, b, and c are in continued proportion.

Mathematically, this relationship is expressed as:

a : b = b : c

We can also write this using fractions:

$ \frac{a}{b} = \frac{b}{c} $

Calculation: Third Proportional to 8 and 12

In this problem, we are given the first two numbers: a = 8 and b = 12. Our goal is to find the third proportional, c.

Step 1: Setting up the Proportion Equation

We substitute the given values into the proportion formula:

8 : 12 = 12 : c

Converting this ratio into a fractional equation gives us:

$ \frac{8}{12} = \frac{12}{c} $

Step 2: Solving for the Unknown (c)

To find the value of c, we can use cross-multiplication. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction:

$ 8 \times c = 12 \times 12 $

First, calculate the product on the right side:

$ 8c = 144 $

Now, to find c, we need to divide both sides of the equation by 8:

$ c = \frac{144}{8} $

Performing the division:

$ c = 18 $

Conclusion

The calculation shows that the value of c is 18. Therefore, the third proportional to 8 and 12 is 18.