maths problem

Cleat Eastwood

ok brainy bikers, my niece came home with a mock sats paper and asked for help on a puzzle such as this

__4__
x 6
_____
2052

whereby you have to deduce the blanks so a 3 digit figure multiplied by 6 gives the answer 2052. I explained that being the 6 times table there are only 2 digits, when multiplied by 6, that will have a 2 in the answer (namely 2 and 7), and that its just a matter, from therein, of trial and error. But is it?

Is there a formula or a way to conceptualise the problem that would help with other perhaps more taxing blank space problems?

Come on brainy chaps, if we can put a man on the moon surely this is not beyond us.

skyd0g

can't you just divide 2052 by 6 = 342 8)

Cleat Eastwood

good grief, so you can, she also has some with blank space answers, I shall see if such a method can be applied. Many thanks skydog, she's only ten and a bit baffled by sums and stuff.

redvee

Cleat Eastwood wrote:

she's only ten and a bit baffled by sums and stuff.

Looks like her uncle is also TBH so would I.

skyd0g

By my reckoning, that's a donut you owe me.

Cleat Eastwood

I wouldnt disagree redvee and since i'm so bad at maths make that 2 donuts. thanks again.

mrushton

mmmmmmmmmmmmmmmm 2 donuts

hopper1

Cleat Eastwood wrote:

ok brainy bikers, my niece came home with a mock sats paper and asked for help on a puzzle such as this

__4__
x 6
_____
2052

whereby you have to deduce the blanks so a 3 digit figure multiplied by 6 gives the answer 2052. I explained that being the 6 times table there are only 2 digits, when multiplied by 6, that will have a 2 in the answer (namely 2 and 7), and that its just a matter, from therein, of trial and error. But is it?

Is there a formula or a way to conceptualise the problem that would help with other perhaps more taxing blank space problems?

Come on brainy chaps, if we can put a man on the moon surely this is not beyond us.

I was watching Discovery the other day, trying to disprove that we did land on the Moon!
Maybe that's why the maths is so hard! :shock:

crumbschief

James Brolin was good in that film.

nolf

Formula in general to answer all questions of this nature is that if you have 2 out of 3 factors in an equation you can find the answer.

e.g 3+x=5

You isolate the missing "x" (x stands for any blank space) on 1 side of the equation.

So 3 + x = 5.

As you're trying to get the x on 1 side, you take away 3 from both sides.

End up with 3+x (-3) = 5 - 3
or x = 5-3
x=2

It's an important basis for working out a whole range of further problems.

More difficult one like that.

x = something with a 4 in

x multiplied by 6 = 2052.
divide by 6 on both sides =

x times 6/6= 2052/6
x=342.

It's important that she understands the basic fundamental of these problems.
In this example the 4 is a useful guide to check you have the correct answer, but should be ignored until you've worked through the problem.

When studying more complex Algebra in high school, it's important you can do that kind of work. Isolating an unknown variable (X) on 1 side of the equation, by doing things simultaneously to both sides.

Good luck to her in her SAT's![/i]

Ben6899

Good post nolf.

It winds me up when people (I use the word loosely) complain "why did they teach us algebra at school? We never use it again."

Erm you use it every day I think you'll find. Just you're not bright enough to realise.

bompington

Ben6899 wrote:

Good post nolf.

It winds me up when people (I use the word loosely) complain "why did they teach us algebra at school? We never use it again."

Erm you use it every day I think you'll find. Just you're not bright enough to realise.

It should be obvious after this that the reason you learn algebra at school is that in time, you can help your kids do their algebra at school

Ben6899

It helps for that as well!

Flasheart

crumbschief wrote:

James Brolin was good in that film.

Capricorn One?

TurboMonkey

Just like long division:

What whole number of the order 10^3 times 6 is close to or equal but not greater than 2052?
None.

What whole number of the order 10^2 times six is close to or equal but not greater than 2052?
Three, as 300 x 6 is 1800

What whole number of the order 10^1 times six is close to or equal but not greater than 2052 -1800 (252) ?
4, as 40 x 6 = 240

What whole number of the order 10^0 times six is close to or equal, but not greater than 252-240 (12) ?
2 as 2 x 6 = 12 as this is equal to the remainder the answer (342) is complete

If you have a remainder after getting to order one; keep lowering the power (moving the decimal place to the left) and doing the same for each iteration until you get as accurate as you want.


This can work algebraically, or numerically, or even using a number system which uses a different base.

garrynolan

skyd0g wrote:

can't you just divide 2052 by 6 = 342 8)

That's how I would do it.

garrynolan

TurboMonkey wrote:

Just like long division:

What whole number of the order 10^3 times 6 is close to or equal but not greater than 2052?
None.

What whole number of the order 10^2 times six is close to or equal but not greater than 2052?
Three, as 300 x 6 is 1800

What whole number of the order 10^1 times six is close to or equal but not greater than 2052 -1800 (252) ?
4, as 40 x 6 = 240

What whole number of the order 10^0 times six is close to or equal, but not greater than 252-240 (12) ?
2 as 2 x 6 = 12 as this is equal to the remainder the answer (342) is complete

If you have a remainder after getting to order one; keep lowering the power (moving the decimal place to the left) and doing the same for each iteration until you get as accurate as you want.


This can work algebraically, or numerically, or even using a number system which uses a different base.

QueTF????? My God, but that was convoluted! What does the ^ represent?

Buckled_Rims

There's a very simple why to do it, draw it as a triangle. Put the multiplication at the bottom.

2052
342 * 6

Then put your thumb over the missing number to reveal the formula for the answer!

in this case

2052
_4_ * 6

would show as

2052

---

.....................= 342
6

TurboMonkey

The ^ means power, the amount of times a number is multiplied by itself.

Like 2^2 = 4 , 5^2 = 25 , 3^3 = 27 etc.

So above is like:

How many 6000's in that number?
then how many 600's?
then how many 60's in whats left
then how many 6's in whats left from that

This gets the bigger multiples out of the quotient, i'm sure its the same as when you divide things in your head.

I suppose you could deal with smaller numbers by breaking the 6 down into a product of its primes and then multiplying by their reciprocals

6 is 2 x 3
Dividing by 6 is the same as multiplying by 1/6th which is the same as 1/2 x 1/3

2052 x half = 1026
1026 x a third = 342

Hope that helps

garrynolan

garrynolan wrote:

skyd0g wrote:

can't you just divide 2052 by 6 = 342 8)

That's how I would do it.

I do it like this.... 6 into 20 = 3 , carry 2 left over - 6 into 25 = 4, carry 1 left over - 6 into 12 = 2. Answer is 342. Simples!