To break down the division of 6841 by 30 into smaller, friendly equations, we can approach it by using simpler numbers that can be successively combined. Here’s one way to do it:
-
Break down 6841:
- \( 6841 = 6000 + 800 + 40 + 1 \)
-
Divide each component by 30:
- \( 6000 \div 30 = 200 \)
- \( 800 \div 30 = 26 \quad \text{(with a remainder of 20)} \)
- \( 40 \div 30 = 1 \quad \text{(with a remainder of 10)} \)
- \( 1 \div 30 = 0 \quad \text{(with a remainder of 1)} \)
-
Sum of the results without remainders:
- \( 200 + 26 + 1 + 0 = 227 \)
-
Combine remainders:
- Remainders: 20 (from 800) + 10 (from 40) + 1 (from 1) = 31, which is not a complete part of 30.
To encapsulate it all, here are the friendly equations:
- \( 6000 \div 30 = 200 \)
- \( 800 \div 30 = 26 \) (R: 20)
- \( 40 \div 30 = 1 \) (R: 10)
- \( 1 \div 30 = 0 \) (R: 1)
- Combine integers: \( 200 + 26 + 1 + 0 = 227 \)
- Remainders: \( 20 + 10 + 1 = 31 \)
Since divisions yield whole numbers and integers, here's the complete perspective on it:
- \( 6800 \div 30 = 226 \)
- \( 41 \div 30 = 1 \) (R: 11)
- \( 6840 \div 30 = 228 \)
- \( 1 \div 30 = 0 \) (R: 1)
The main takeaway is that \( 6841 \div 30 = 228 \) remainder \( 11 \) after all the smaller calculations sum up correctly.
Thus, you end up with \( 6841 = 30 \times 228 + 11 \).