Question

77 × 412
round 77 to _____.
round 412 to _____.
multiply ___ × _ = ___.

Explanation:

Step1: Round 77

To round 77 to a reasonable number for estimation, we can round it to the nearest ten or hundred. Rounding to the nearest ten, 77 is closer to 80 (since 77 - 70 = 7 and 80 - 77 = 3, so 80 is closer). Alternatively, rounding to the nearest hundred, 77 is closer to 100? Wait, no, 77 is between 0 and 100, and 77 is 23 away from 100 and 7 away from 80 (if rounding to tens) or 77 is 77 away from 0 and 23 away from 100. Wait, maybe the problem expects rounding to the nearest ten or a more convenient number. Let's see, 77 is close to 80 (nearest ten) or 100? Wait, maybe the standard is to round to the nearest ten or hundred. Let's check 77: the tens digit is 7, the ones digit is 7, which is more than 5, so round up the tens digit: 7 + 1 = 8, so 80. So round 77 to 80.

Step2: Round 412

Now, 412: let's round to the nearest hundred or ten. If we round to the nearest hundred, 412 is closer to 400 (since 412 - 400 = 12 and 500 - 412 = 88, so 400 is closer). Alternatively, nearest ten: 410, but maybe rounding to the nearest hundred is better for estimation. So round 412 to 400.

Step3: Multiply the rounded numbers

Now, multiply the rounded numbers: 80 × 400. Let's calculate that. 80 × 400 = 80 × 4 × 100 = 320 × 100 = 32000.

Answer:

Round 77 to $\boldsymbol{80}$.
Round 412 to $\boldsymbol{400}$.
Multiply $\boldsymbol{80} \times \boldsymbol{400} = \boldsymbol{32000}$.

(Note: Alternatively, if we round 77 to 100 and 412 to 400, we get 100×400=40000, but 80 is a closer round for 77. The most common estimation here would be rounding 77 to 80 and 412 to 400.)