To divide 405 in the ratio 3:12, we follow these steps:

Step 1: Calculate the total parts in the ratio

The total parts in the ratio $3:12$ is the sum of 3 and 12: $3 + 12 = 15 \text{ parts}$

Step 2: Find the value of each part

To find the value of each part, divide the total (405) by the total number of parts (15): $\text{Value of each part} = \frac{405}{15} = 27$

Step 3: Calculate the individual amounts

• The first part, corresponding to the ratio 3, is: $3 \times 27 = 81$
• The second part, corresponding to the ratio 12, is: $12 \times 27 = 324$

Final answer

So, the division of 405 in the ratio 3:12 is: $81 \text{ and } 324$

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you divide 500 in the ratio 4:6?
2. What is the sum of two numbers in the ratio 5:7 if the total is 720?
3. Can a ratio be expressed in its simplest form? How would you simplify 8:12?
4. If you reverse the numbers in a ratio, does the result change? Why or why not?
5. How do you solve a ratio when fractions are involved, like 1/2 : 3/4?

Tip: When solving ratios, always check if the numbers can be simplified before performing calculations.