Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (2) of the multiplier 532 by each digit of the multiplicand 752, from right to left.
Multiply the ones digit (2) of the multiplicator by the number in the ones place value:
2×2=4
Write 4 in the ones place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 4 | ||||||
Multiply the ones digit (2) of the multiplicator by the number in the tens place value:
2×5=10
Write 0 in the tens place.
Because the result is greater than 9, carry the 1 to the hundreds place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | ||||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 0 | 4 | |||||
Multiply the ones digit (2) of the multiplicator by the number in the hundreds place value and add the carried number (1):
2×7+1=15
Write 5 in the hundreds place.
Because the result is greater than 9, carry the 1 to the thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | |||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
1,504 is the first partial product.
Proceed by multiplying the tens digit (3) of the multiplier (532) by each digit of the multiplicand (752), from right to left.
Because digit (3) is in tens place, we shift partial result by 1 place(s) by placing 1 zero(s).
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 0 | ||||||
Multiply the tens digit (3) of the multiplicator by the number in the ones place value:
3×2=6
Write 6 in the tens place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 6 | 0 | |||||
Multiply the tens digit (3) of the multiplicator by the number in the tens place value:
3×5=15
Write 5 in the hundreds place.
Because the result is greater than 9, carry the 1 to the thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | ||||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 5 | 6 | 0 | ||||
Multiply the tens digit (3) of the multiplicator by the number in the hundreds place value and add the carried number (1):
3×7+1=22
Write 2 in the thousands place.
Because the result is greater than 9, carry the 2 to the ten thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 2 | 1 | |||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 2 | 2 | 5 | 6 | 0 | ||
22,560 is the second partial product.
Proceed by multiplying the hundreds digit (5) of the multiplier (532) by each digit of the multiplicand (752), from right to left.
Because digit (5) is in hundreds place, we shift partial result by 2 place(s) by placing 2 zero(s).
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 2 | 2 | 5 | 6 | 0 | ||
| 0 | 0 |
Multiply the hundreds digit (5) of the multiplicator by the number in the ones place value:
5×2=10
Write 0 in the hundreds place.
Because the result is greater than 9, carry the 1 to the thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | ||||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 2 | 2 | 5 | 6 | 0 | ||
| 0 | 0 | 0 |
Multiply the hundreds digit (5) of the multiplicator by the number in the tens place value and add the carried number (1):
5×5+1=26
Write 6 in the thousands place.
Because the result is greater than 9, carry the 2 to the ten thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 2 | 1 | |||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 2 | 2 | 5 | 6 | 0 | ||
| 6 | 0 | 0 | 0 |
Multiply the hundreds digit (5) of the multiplicator by the number in the hundreds place value and add the carried number (2):
5×7+2=37
Write 7 in the ten thousands place.
Because the result is greater than 9, carry the 3 to the hundred thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 2 | 1 | ||||
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 2 | 2 | 5 | 6 | 0 | ||
| 3 | 7 | 6 | 0 | 0 | 0 |
376,000 is the third partial product.
3. Add the partial products
1504+22560+376000=400064 long addition steps can be seen here
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 7 | 5 | 2 | ||||
| × | 5 | 3 | 2 | |||
| 1 | 5 | 0 | 4 | |||
| 2 | 2 | 5 | 6 | 0 | ||
| + | 3 | 7 | 6 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 6 | 4 |
The solution is: 400,064
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