Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (5) of the multiplier 3,285 by each digit of the multiplicand 1,257, from right to left.
Multiply the ones digit (5) of the multiplicator by the number in the ones place value:
5×7=35
Write 5 in the ones place.
Because the result is greater than 9, carry the 3 to the tens place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | |||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 5 | |||||||
Multiply the ones digit (5) of the multiplicator by the number in the tens place value and add the carried number (3):
5×5+3=28
Write 8 in the tens place.
Because the result is greater than 9, carry the 2 to the hundreds place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 2 | 3 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 8 | 5 | ||||||
Multiply the ones digit (5) of the multiplicator by the number in the hundreds place value and add the carried number (2):
5×2+2=12
Write 2 in the hundreds place.
Because the result is greater than 9, carry the 1 to the thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 3 | |||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 2 | 8 | 5 | |||||
Multiply the ones digit (5) of the multiplicator by the number in the thousands place value and add the carried number (1):
5×1+1=6
Write 6 in the thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 3 | |||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
6,285 is the first partial product.
Proceed by multiplying the tens digit (8) of the multiplier (3,285) by each digit of the multiplicand (1,257), from right to left.
Because digit (8) is in tens place, we shift partial result by 1 place(s) by placing 1 zero(s).
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 0 | |||||||
Multiply the tens digit (8) of the multiplicator by the number in the ones place value:
8×7=56
Write 6 in the tens place.
Because the result is greater than 9, carry the 5 to the hundreds place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 5 | |||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 6 | 0 | ||||||
Multiply the tens digit (8) of the multiplicator by the number in the tens place value and add the carried number (5):
8×5+5=45
Write 5 in the hundreds place.
Because the result is greater than 9, carry the 4 to the thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 4 | 5 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 5 | 6 | 0 | |||||
Multiply the tens digit (8) of the multiplicator by the number in the hundreds place value and add the carried number (4):
8×2+4=20
Write 0 in the thousands place.
Because the result is greater than 9, carry the 2 to the ten thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 2 | 4 | 5 | |||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 0 | 5 | 6 | 0 | ||||
Multiply the tens digit (8) of the multiplicator by the number in the thousands place value and add the carried number (2):
8×1+2=10
Write 0 in the ten thousands place.
Because the result is greater than 9, carry the 1 to the hundred thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 4 | 5 | ||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
100,560 is the second partial product.
Proceed by multiplying the hundreds digit (2) of the multiplier (3,285) by each digit of the multiplicand (1,257), from right to left.
Because digit (2) is in hundreds place, we shift partial result by 2 place(s) by placing 2 zero(s).
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 0 | 0 | ||||||
Multiply the hundreds digit (2) of the multiplicator by the number in the ones place value:
2×7=14
Write 4 in the hundreds place.
Because the result is greater than 9, carry the 1 to the thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | |||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 4 | 0 | 0 | |||||
Multiply the hundreds digit (2) of the multiplicator by the number in the tens place value and add the carried number (1):
2×5+1=11
Write 1 in the thousands place.
Because the result is greater than 9, carry the 1 to the ten thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 1 | 4 | 0 | 0 | ||||
Multiply the hundreds digit (2) of the multiplicator by the number in the hundreds place value and add the carried number (1):
2×2+1=5
Write 5 in the ten thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 5 | 1 | 4 | 0 | 0 | |||
Multiply the hundreds digit (2) of the multiplicator by the number in the thousands place value:
2×1=2
Write 2 in the hundred thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
251,400 is the third partial product.
Proceed by multiplying the thousands digit (3) of the multiplier (3,285) by each digit of the multiplicand (1,257), from right to left.
Because digit (3) is in thousands place, we shift partial result by 3 place(s) by placing 3 zero(s).
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
| 0 | 0 | 0 |
Multiply the thousands digit (3) of the multiplicator by the number in the ones place value:
3×7=21
Write 1 in the thousands place.
Because the result is greater than 9, carry the 2 to the ten thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 2 | |||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
| 1 | 0 | 0 | 0 |
Multiply the thousands digit (3) of the multiplicator by the number in the tens place value and add the carried number (2):
3×5+2=17
Write 7 in the ten thousands place.
Because the result is greater than 9, carry the 1 to the hundred thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
| 7 | 1 | 0 | 0 | 0 |
Multiply the thousands digit (3) of the multiplicator by the number in the hundreds place value and add the carried number (1):
3×2+1=7
Write 7 in the hundred thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
| 7 | 7 | 1 | 0 | 0 | 0 |
Multiply the thousands digit (3) of the multiplicator by the number in the thousands place value:
3×1=3
Write 3 in the millions place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | ||||||
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
| 3 | 7 | 7 | 1 | 0 | 0 | 0 |
3,771,000 is the fourth partial product.
3. Add the partial products
6285+100560+251400+3771000=4129245 long addition steps can be seen here
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 2 | 5 | 7 | ||||
| × | 3 | 2 | 8 | 5 | |||
| 6 | 2 | 8 | 5 | ||||
| 1 | 0 | 0 | 5 | 6 | 0 | ||
| 2 | 5 | 1 | 4 | 0 | 0 | ||
| + | 3 | 7 | 7 | 1 | 0 | 0 | 0 |
| 4 | 1 | 2 | 9 | 2 | 4 | 5 |
The solution is: 4,129,245
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