47385 x 25. How?

[pukkapine]

Homework... DS attempted (and succeeded) in correctly answering this using the 'grid method' that I had never seen before. It seemed very convoluted?? How would your child approach this and how old/NC level/year group?(having a few concerns re his maths with regards to gaps in his learning).

[Martorana]

He's older and in bed so I can't ask- but I am sure that at this age, my ds would have multiplied by 100 and divided by 4.

I have no idea whether that's an "approved" method or not- but that's wh the would have done.

[Ruprekt]

Love the grid method! Split the 25 into 20 and 5 to do the multiplication.

Much easier than when we were kids.

[ouryve]

Is that what it's called? I'd add a nought, double it (to get 20x), halve it (to get 5x) and add the two together. Used to call that chunking.

[coco44]

x100
divide by 4
yr4

[LowCloudsForming]

Grid is a visual method for chunking.

[pukkapine]

Yep I suggested x100 divide by 4. He could multiply by 100 but then didn't know how to divide by four so chose the grid method instead. Which seems harder to me...

[squiggletea]

half and half again to divide by 4

[Menolly]

My sister (9) would do:

47385 x 2 then times that by 10
47385 x 5 then add the 2 answers together.

[PeasandCucumbers]

If I was working this out I would break down the 25 and do

10 x 47385 = 473,850
10 x 47385 = 473,850
5 x 47385 = 236,925
25 x 47385 = 1,184,625

Or just do long multiplication set out like this

47,385
X 25
1,184,625

[TeenAndTween]

dd2 y4 would say she couldn't do it.
I would then remind her about the grid method and she would do it, but probably make a mistake or 3.

dd1 y10 probably also wouldn't spot the multiply by 100, divide by 4 method.
She would use a calculator, or if not allowed she would use the grid method and get it right. (She's never mastered the shorter long multiplation, and it's not holding her back particularly)

In my head I did divide by 4 then multiply by 100.

If I had to do it on paper and show working I would possibly have gone for long multiplication (multiply by 20 and by 5 and add).

In our school they move off the grid method in y5/y6.

[columngollum]

2x10+1x5

[reddidi]

This question is only suitable for practicing long multiplication.

There are too many digits and the multiplier is not divisible by 4 so the x 100 ÷ 4 mental short cut is too hard.

Chunking (473850 + 473850 +236925) is also too hard because of the '73' digits making mental division by 2 difficult.

And the grid method is unsuitable for numbers with this many digits - you need to calculate 12 separate products and add them together!

[coco44]

This question is only suitable for practicing long multiplication

No it isn't you shove 2 noughts on the end and then divide by 4 using short division (see below).I can do it easily in my head writing/calling the digits of the answer as I go and I am not particularly numerate
4 /4 1
7/4 1
33/4 8
18/4 4
25/4 6
10/4 2
20/4 5

[AllergyMums]

Yr 4? Really...oh my head hurts.

[PastSellByDate]

pukkapine:


47,385 X 25

grid method is long winded - but splits it up into easier units for the child:

so 25 - split into 20 and 5

47,385 - split into 40,000 - 7,000 - 300 - 80 - 5

This is effectively splitting out the 'places' (ten thousands/ thousands/ hundred/ tens and units) - and then working out multiplications that are easily achieved because your either multiplying units (so recalling timestable facts) or multiplying tens+.

To be honest at this point (when numbers got bigger than 2/3 digits) I just found it faster to use vertical column method of multiplication are then just recall multiplication facts and remember to add '0' or '0s' in as you moved along from units to tens, etc...


Grid method:

Multiplying 5 x 40,000/ 7,000/ 300/ 80/ 5 (5 operations)
Multiplying 20 x 40,000/ 7,000/ 300/ 80/ 5 (5 operations)
Adding resulting products together: 5 operations (by place value - so adding ten thousands results/ thousand results/ etc...)
Adding all products together to recompose the number: 4 operations

TOTAL: 19 mathematical calcualtions or operations

Column method

10 multiplying operations - same as above in effect (but just multiplying single digits and carrying over if product >9 - effectively multiplying 5 x 5/ 5 x 8/ 5 x 3/ 5 x 7/ 5 x 4 - which all may seem easier if you know your times tables - then same idea with x2 (but putting in a place holder zero in the units column - first column on right under the 5 - resulting from 5 x 5)

5 additions: because your multiplying by 25 (two digits) there are two rows of digits to add up

15 operations.

Less work at this point to do it by column method - and if multiplication facts are sound - it can be quicker as well.

---------

I liked the coco44 answer - x100 and then divide by 4.

If your DC is too young to know how to divide yet - this can be thought of as x100/ halve (which = x50) and halve again (which = x25).

47,385 x 100 = 4,738,500 and this may be too tricky to divide in half and then 1/4 as a whole number

so split it up:

4,000,000 - 1/2 is 2,000,000 and 1/2 of that = 1,000,000
700,000 - 1/2 is 350,000 and 1/2 of that is 175,000
30,000 - 1/2 is 15,000 and 1/2 of that is 7,500
8000 - 1/2 is 4000 and 1/2 of that is 2000
500 - 1/2 of that is 250 and 1/2 of that is 125

add up 1,000,000 + 175,000 = 1,175,000
add 1,175,000 + 7,500 = 1,182,500
add 1,182,500 + 2000 = 1,184,500
add 1,184,500 + 125 = 1,184,625

(but again adding in a column is faster than horizontally mentally adding these 5 numbers).

---------

My view is that knowing these different methods doesn't hurt - sometimes knowing how to 'decompose' or 'deconstruct' large numbers becomes helpful - when you're dividing for example (like coco44 showed with knowing that 25 x 4 = 100 so multipling a number (say A) by 100 and dividing by 4 will give you 25 x that number A - but ultimately for speed - traditional column method will win out the larger the numbers are that you are working with.

HTH

[pukkapine]

Thanks all. Much appreciated. I think DS, who is highly able at maths for his age, struggles to know which method to use when, coupled with the fact he hasn't been taught some methods. he can come up with the answer but not necessarily knowing how he did it, or not in the most direct way.