<span>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!</span>
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).
