Third Proportional Calculation for 45 and 60

The question asks us to find the third proportional of two numbers, 45 and 60. Let the third proportional be denoted by x.

Understanding Third Proportional

When three numbers are in proportion, the ratio of the first number to the second number is equal to the ratio of the second number to the third number. If a, b, and x are in proportion, it means:

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

In this problem, we are given a = 45 and b = 60. We need to find the third proportional, x.

Step-by-Step Calculation

1. Set up the proportion: Based on the definition, we can write the proportion using the given numbers and x: $ \frac{45}{60} = \frac{60}{x} $
2. Cross-multiplication: To solve for x, we cross-multiply the terms: $ 45 \times x = 60 \times 60 $
3. Calculate the product: First, calculate the product on the right side: $ 45x = 3600 $
4. Solve for x: Now, isolate x by dividing both sides of the equation by 45: $ x = \frac{3600}{45} $
5. Simplify the fraction: We can simplify the fraction $\frac{3600}{45}$. Let's divide both the numerator and the denominator by common factors. Both are divisible by 5: $ x = \frac{3600 \div 5}{45 \div 5} = \frac{720}{9} $ Now, divide 720 by 9: $ x = 80 $

Conclusion

The value of the third proportional, x, is 80.