Show how to solve the problem \(378 \times 6\) using place value with regrouping. Explain how you knew when to regroup.

Answer
2,268
Explanation




By grouping 378 ca n be written as,
378 = 300 + 70 + 8
6× 378 = 6 × (300 + 70 + 8)
= (6×300)

(6×70) + (6×8)

= 1800 + 420 + 48
= 2,268

Answered by smmwaite | 2024-06-11

To solve the problem 378 x 6 using place value with regrouping, we begin by multiplying the ones place. So, 8 (ones) times 6 equals 48. Since 48 has more than one digit, we write the 8 in the ones place of our answer and regroup the 4 (which represents 40) into the tens place.
Next, we multiply the tens place. 7 (tens) times 6 equals 42, plus the 4 we regrouped makes 46 tens or 460. We write down the 6 in the tens place of our answer and regroup the 4 (now representing 400) to the hundreds place.
Finally, we multiply 3 (hundreds) by 6, which equals 18 hundreds or 1800, then add the 4 hundred we regrouped for a total of 22 hundreds or 2200. We add these to our answer for a final result of 2268.
We knew when to regroup because any product over 9 in an individual place value needs to be broken into the next higher place value. Thus, in multiplying by 6, we watched for products over 9 in the ones and tens places.

Answered by EzraMatthewMiller | 2024-06-24

The product of 378 × 6 using place value with regrouping is 2268 . We break down 378 into 300 + 70 + 8 and multiply each component by 6 , then add the results. Regrouping is required when sums in a given place value exceed 9, but this specific multiplication did not require regrouping during addition.
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Answered by smmwaite | 2024-09-04