Today we'll learn how to calculate 3000 divided by 125 divided by 8 using a simple method. Instead of doing the divisions one by one, we can use the division property to combine the divisors first, making the calculation much easier.
Let's understand why this method works. The division property tells us that when we divide by multiple numbers in sequence, we can instead divide by their product. This is because division is the inverse operation of multiplication. When we divide by 125 and then by 8, it's equivalent to undoing multiplication by these numbers in reverse order.
Now we need to calculate 125 times 8. There are several ways to do this. The direct multiplication gives us 1000. We can also recognize that 125 is one-eighth of 1000, so 125 times 8 equals 1000. Another approach is to see that 8 equals 2 cubed, so we can multiply 125 by 2 three times: 250, then 500, then 1000.
Now we can perform the final calculation. We have 3000 divided by 1000, which is much easier to compute. We can write this as a fraction: 3000 over 1000. This simplifies to 3 times 1000 over 1000, which equals 3 times 1, giving us our final answer of 3. We can verify this by checking that 3 times 125 times 8 equals 3000.
To summarize, we solved 3000 divided by 125 divided by 8 by using the division property to combine the divisors first. This gave us 3000 divided by 1000, which equals 3. The key insight is to look for numbers that multiply to powers of 10, making division much simpler. This technique works for many similar problems, such as 2400 divided by 25 divided by 4, or 5000 divided by 50 divided by 2.