Question

What two partial products would you add to find 513 x 46

Answer 1

First, let me do the Mathematical part of that, and then I shall explain the theory behind it.

Mathematical part:
We are going to multiply 513 with 46. So the two partial products that we are going to choose are 40 and 6.

Multiply 513 with 6 first.

513
x46
--------------------------
18 (as 6*3 = 18)
60 (as 6*10 = 60; In 513, the digit at tenths place is 1, so 1*10=10)
3000 (as 6*500 = 3000; In 513, 5 is at hundredth place, so 5*100=500)
120 (as 40*3 = 120; since 4 is at the tenth place, so 4*10=40)
400 (as 40*10 = 400)
20000 (as 40*500 = 20000)
--------------------------
23598 (Add all of them)


Theory:
As you can see above that we have chosen the two partial products individually which are 6 and 40. Since 4 in 46 is in tenth place, we have to consider it 40 (since 4*10 = 40). One by one, we first multiply 6 with 513. Then we move to the tenth place, and multiply 513 with 40. At the end, we have added all the results we found after multiplication.

Check: If we check the multiplication result by using the calculator, we would get the same result (23598).

Another Method (instant):
513 * (40+6) = (513*40) + (513*6) = 23598.

Answer 2

We know that 46 = 40 + 6. So one partial product would be: 513 x 40 = ( 500 x 40 ) + ( 10 X 40 ) + ( 3 x 40 ) = 20 000 + 400 + 120 = 20,520. Another partial product: 513 x 6 = ( 500 x 6 ) + ( 10 x 6 ) + ( 3 x 6 ) = 3 000 + 60 + 18 = 3,078. Finally: 20,520 + 3.078 = 23,598. And we can check it: 513 * 46 = 23,598. Hope this helps. Let me know if you need additional help!