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Q: Explain why second partial product is always greater than the first partial priduct when you multiply two 2-digit numbers?

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The answer will depend on the order in which you do partial products. It is quite common in the UK for the first partial product to be the two digits in the tens' place and so that is often the largest. This ties in with the method for multiplying two binomials when they move on to algebra.

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First, you look at the hundreds place( if there are any) then you multiply those together. Put that off to the side. Next do the same process until you get to the ones. When you are finished multiplying them, you add all of the numbers that you put off to the side, and then you get your answer.

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Partial sums is actually use for addition while partial products is used for multiplication. With partial sums, numbers above nine are added together in the tens, hundreds, etc. columns first. Individual sums are then added together for the final sum.

Instead of having to do multiples of two numbers with several digits in each, all you need to be able to do is to multiply pairs of 1 digit numbers, add the correct number of 0s for powers of tens, and then add together a string of numbers. Actually, all that sounds a lot more complicated than it is. It may be easier to explain with an example: 567*89 Adding Partial products: (500*80 + 500*9 + 60*80 + 60*9 + 7*80 + 7*9) = 40000 + 4500 + 4800 + 540 + 560 + 63 = 50463

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