using powers of 10, which would be the best choice for the first number to subtract in the division problem 742 divided by 61
The Correct Answer and Explanation is:
To solve 742 ÷ 61 using powers of 10, the best choice for the first number to subtract is 610, which is 61 × 10.
This method is known as partial quotients division, and it breaks down a division problem into easier steps using multiples of the divisor.
Step-by-step:
- Recognize that 61 × 10 = 610 is a close, manageable multiple of 61 that is still less than 742.
- Subtract 610 from 742: 742−610=132742 – 610 = 132742−610=132
- Now divide what’s left, 132, by 61. The largest multiple of 61 less than or equal to 132 is 122, which is 61 × 2.
- Subtract again: 132−122=10132 – 122 = 10132−122=10
- Now we’re left with 10, which is smaller than 61. This means it’s the remainder.
- Add the partial quotients: 10 (from step 1) plus 2 (from step 3) equals 12, with a remainder of 10.
Final Answer:
742 ÷ 61 = 12 remainder 10, or 12 R10
Explanation:
When using powers of 10 in division, especially in mental math or estimation, we look for large chunks that are easy to subtract and still efficient. Since 61 is the divisor, starting with 61 × 10 is a smart move because it gets us close to the dividend, 742, without overshooting it.
Trying a larger multiple like 61 × 20 = 1220 would overshoot 742, and 61 × 5 = 305 would work but not take as much out of the dividend initially. By using the biggest multiple possible without exceeding 742, we reduce the number of steps needed.
This strategy makes the division easier, especially when teaching or doing long division without a calculator.
