To calculate the product of 513 and 46 using the partial products method, you can break it down into the following steps:
Multiply 6 (the units digit of 46) by each digit of 513, one at a time, and write down the results:
6 * 3 = 18 (Write down 8, carry over 1)
6 * 1 = 6 + 1 (Carry over from the previous step) = 7 (Write down 7)
Multiply 40 (the tens digit of 46, considering its place value) by each digit of 513, one at a time, and write down the results, shifted one position to the left:
40 * 3 = 120 (Write down 0, carry over 12)
40 * 1 = 40 + 12 (Carry over from the previous step) = 52 (Write down 52)
Multiply 500 (the hundreds digit of 46, considering its place value) by each digit of 513, one at a time, and write down the results, shifted two positions to the left:
500 * 3 = 1500 (Write down 0, carry over 150)
500 * 1 = 500 + 150 (Carry over from the previous step) = 650 (Write down 650)
Now, add up all the partial products:
⬇️
18
7 (Carry over from the previous step)
0 (Carry over from the previous step)
52
+650
23598
So, 513 x 46 = 23,598 using the partial products method.