Math Is Fun Forum

Casi

Member

Registered: 2009-03-06

Posts: 4

Missing factors in multiplication

Hi

I have some basic multiplication question: ?x3x10=150

I know the answer is 5. I know that I can divide 150 by 10 and get 15 and then divide that by 3 to get 5.

However, I have to work this out without using mental arithmetic or division. I have to use a a pyramid to get the answer. However, it needs to be down to the lowest numbers. For example. For the sum above, I have to do this:
nx3x10
    3x10=30
5x30=
150
n=5

However, I am not allowed to do the sum at this level. I have to find a way of breaking down the sum 5x30=150 so that I'm using numbers up to 10 only so basically, I need to arrive at the answer 5 using lower numbers than 11. I am not allowed to use division.

Any ideas?

Just to confirm. Removing zeros isn't going to work as not all the sums have zeros to drop...

Thanks:)

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: Missing factors in multiplication

Hmm... Could you give me an example on how the pyramid should look like?

Numbers below 10?
The prime factors of 150 is 1 x 2 x 3 x 5 x 5

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

Casi

Member

Registered: 2009-03-06

Posts: 4

Re: Missing factors in multiplication

I'll try. Here is another example

So another example I have is nx8x3=48, so:
...    ?     x    8    x    3                                         
...                     =24
...           ?   x    24
...              =48

So answer is 2 but I'm not allowed to say what x 24=48 because it involves using the 12 times table and I can only go up to the 10 times table.

Thanks:)

Last edited by Casi (2014-12-03 02:58:54)

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: Missing factors in multiplication

Only to the ten times table?
... 5    3  5    2
...   15      10
...       150

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: Missing factors in multiplication

hi Casi

Assuming there is an answer (eg.  ? x 17 x 19 = 4199 would not have a solution using only factors less than ten).

By keeping the factors close to each other you'd avoid large factors.

eg.  48

√48  ≈ 6.9 so start by checking if 6 is a factor; it is so you'll get 6 x 8 straight away.

Even this isn't fool proof though:

eg.  ? x 5 x 13 = 195

√195  ≈ 13.9

so check 13 first:  13 x 15 = 195.

Perhaps you could state the exact wording of the problem, or what it is you are trying to make.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob