Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (4) of the multiplier 34 by each digit of the multiplicand 514, from right to left.
Multiply the ones digit (4) of the multiplicator by the number in the ones place value:
4×4=16
Write 6 in the ones place.
Because the result is greater than 9, carry the 1 to the tens place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | |||||
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 6 | |||||
Multiply the ones digit (4) of the multiplicator by the number in the tens place value and add the carried number (1):
4×1+1=5
Write 5 in the tens place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | |||||
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 5 | 6 | ||||
Multiply the ones digit (4) of the multiplicator by the number in the hundreds place value:
4×5=20
Write 0 in the hundreds place.
Because the result is greater than 9, carry the 2 to the thousands place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 2 | 1 | ||||
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 2 | 0 | 5 | 6 | ||
2,056 is the first partial product.
Proceed by multiplying the tens digit (3) of the multiplier (34) by each digit of the multiplicand (514), 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 | ten thousands | thousands | hundreds | tens | ones |
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 2 | 0 | 5 | 6 | ||
| 0 |
Multiply the tens digit (3) of the multiplicator by the number in the ones place value:
3×4=12
Write 2 in the tens place.
Because the result is greater than 9, carry the 1 to the hundreds place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | |||||
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 2 | 0 | 5 | 6 | ||
| 2 | 0 |
Multiply the tens digit (3) of the multiplicator by the number in the tens place value and add the carried number (1):
3×1+1=4
Write 4 in the hundreds place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | |||||
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 2 | 0 | 5 | 6 | ||
| 4 | 2 | 0 |
Multiply the tens digit (3) of the multiplicator by the number in the hundreds place value:
3×5=15
Write 5 in the thousands place.
Because the result is greater than 9, carry the 1 to the ten thousands place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | ||||
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 2 | 0 | 5 | 6 | ||
| 1 | 5 | 4 | 2 | 0 |
15,420 is the second partial product.
3. Add the partial products
2056+15420=17476 long addition steps can be seen here
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 5 | 1 | 4 | |||
| × | 3 | 4 | |||
| 2 | 0 | 5 | 6 | ||
| + | 1 | 5 | 4 | 2 | 0 |
| 1 | 7 | 4 | 7 | 6 |
The solution is: 17,476
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