Select all correct combinations of partial quotients which can be used to find 74/2
The Correct Answer and Explanation is:
To solve 742\frac{74}{2}274 using the partial quotients method, we break the division into manageable steps. This method involves subtracting multiples of the divisor from the dividend, making it easier to calculate the quotient step by step.
Step-by-Step Solution:
- Starting with 74, subtract multiples of 2:
- 74−20=5474 – 20 = 5474−20=54, so we subtract 2×10=202 \times 10 = 202×10=20 from 74.
- Now, we have 54. Next, we subtract 2×10=202 \times 10 = 202×10=20 again.
- 54−20=3454 – 20 = 3454−20=34, so another partial quotient is 10.
- Continue with the remaining 34:
- Subtract 2×10=202 \times 10 = 202×10=20 from 34.
- 34−20=1434 – 20 = 1434−20=14, so another partial quotient is 10.
- Subtract 2 times 7:
- 14−14=014 – 14 = 014−14=0, so the final partial quotient is 7.
At this point, we have used the following partial quotients: 10, 10, and 7. Summing them up:
- 10+10+7=2710 + 10 + 7 = 2710+10+7=27.
Thus, the quotient of 742\frac{74}{2}274 is 27.
Explanation of Partial Quotients:
- The partial quotients method is designed to simplify division by breaking it into smaller, more manageable steps.
- At each step, we subtract a multiple of the divisor (in this case, 2) from the dividend (74) and keep track of the quotients (which are the multiples of 2 we subtracted).
- This method allows for flexibility, as we can choose different multiples of the divisor to subtract, as long as the approach is systematic.
Correct Combinations:
The partial quotients used to solve 742\frac{74}{2}274 could be any combination that sums to 27, such as:
- 10+10+710 + 10 + 710+10+7
- 20+20+720 + 20 + 720+20+7
- 30+730 + 730+7 All of these are valid combinations, as they represent different ways of subtracting multiples of 2 to reach the final quotient.