- Begin with 184 and subtract \(10 \times 8 = 80\) to leave 104.
- Subtract another \(10 \times 8 = 80\) from 104 to leave 24.
- Subtract the final multiple \(3 \times 8 = 24\) to reach a remainder of 0.
- Sum the partial quotients: \(10 + 10 + 3 = \boxed{23}\).
Explanation
- Analyzing the Division Problem
The problem requires dividing the number 184 by 8 using the method of partial quotients. The dividend is 184, and the divisor is 8. The method of partial quotients involves repeatedly subtracting multiples of the divisor from the dividend until the remainder is zero. The quotient is then the sum of the multipliers used in each subtraction step.
- First Partial Quotient Subtraction
We begin by identifying a large, convenient multiple of 8 to subtract from 184. We know that \(10 \times 8 = 80\). Subtracting 80 from 184 leaves a remainder of \(184 - 80 = 104\). We record the partial quotient of 10.
- Second Partial Quotient Subtraction
Now, we take the remaining 104 and repeat the process. Again, we can subtract another 80 by using the multiple \(10 \times 8 = 80\). The new remainder is \(104 - 80 = 24\). We record another partial quotient of 10.
- Final Subtraction and Quotient Summation
Finally, we look at the remaining 24. We know that \(3 \times 8 = 24\). By subtracting 24 from 24, we reach a remainder of 0. We record the final partial quotient of 3. Adding these partial quotients together, we get \(10 + 10 + 3 = 23\). Thus, \(184 \div 8 = 23\).
Examples
The method of partial quotients is a powerful tool for division, especially when dealing with larger numbers or mental math. For instance, if you are organizing 184 books into 8 boxes, this method helps you quickly determine that each box holds 23 books. By breaking down the total quantity into manageable chunks, you can solve division problems more intuitively without relying on formal long division algorithms.