Multiplying Decimals

[southbucks3]

Our gs is not top of the tree, but always seems to be in the top 50 for results, and they do not teach simultaneous equations until the middle of year 7.

Why the race to learn maths faster than everyone else?

Guest 55 you were in my thoughts in the pub last night...we were working out how far a Yorkshire three peaks walk was in miles, if you included upage and.downage and the chap with us knocked the conversion decimals out, then popped them back in...it made me chuckle. Doubt we got the answer right, but it is a very long way from the proposed b and b in a round trip..may have to review.

[berks_mum]

9 pens and 5 pencils cost £3.20. 7 pens and 8 pencils cost £2.90.
The unit price for each pencil is _____ and pen is _______.

Parents - any ideas on what school would teach 10 yr old to solve this

This is what I am thinking of at the moment. In one of the 11+ papers there was a question -

Two shirts and tree tops cost £29.Three shirts and one top cost £19. What is the cost of a top?

Only thing DD could make out of it was -

2S + 3T = 29
3S + 1T = 19

[JustADadHere]

2s + 3t = 29
3s + 1t = 19

Use the second equation to make 1t = 19 - 3s
Substitute into first equation -> 2s + 3(19-3s) = 29
Simplify and solve:
2s + 57 - 9s = 29
-7s = -28
s = 4

Substitute back into either equation:
3(4) + 1t = 19
12 + 1t = 19
t = 7

Shirts are £4, tops are £7.

There is actually a less complicated way - multiply each equation by a factor and subtract equations.

3(2s+3t=29)
2(3s+1t=19)
to give
6s+9t=87
6s+2t=38

subtract equations:
6s+9t=87
- 6s+2t=38
-------------
7t = 49
t = 7
Substitute back and get s=4

Of course, with wolfram alpha, you can type it in and get a solution in seconds: http://m.wolframalpha.com/input/?i=2s%2 ... 989&y=-126" onclick="window.open(this.href);return false;

[Guest55]

How complicated is that!

There is no need to multiply both equations ... if you multiply the second by 3 you wil make the coefficients of t equal.

It only asks you for the cost of a top - not both!

To be honest with such small numbers I guessed the answer.

[parent2013]

It is a standard simultaneous equation question from Grammar school papers. The reason I posted this question is not about method of solving it. I'm trying to flag the point on poor level of Maths that is taught in the primary schools & big difference in what is expected standard for top GS. Ask any of your Year 4, Year 5 and Year 6 class teachers in State school if they teach simultaneous equations. I guess their answer would be "hit and trial" - which may or may not work with downside that it may take forever.

The questions I have seen that they teach in Year 6 is very basic algebra: For example - Find x
x - 7 = 10

The question arises - is it that the child is not intelligent to pass the GS exam or is he not given the right set of tools and techniques. I think it is the latter. That's where DIY parents and tutors make a difference to facilitate child to clear the finish line - not the school.

[mystery]

Gave these sums to DD.

For first one she did - 5/100 x 360/6 then cross cancellation and came to 30/10 = 3

Second one - 9/100 ÷ 3/1000 then flip the second fraction (her favourite) and cross cancel.

Third - 8/490 x 7 again cross cancel simplifying 8/70 to 4/35 (asked if i wanted her to go further and convert into decimal. I told her not to bother)

Well done. That's exactly what I was trying to say i.e. convert decimal into whole. Therefore 0.05 would become 5/100, then cross cancel zeros, multiply/calculate other numbers, then see how many decimal places to move in the end based on zeros left.

Guest55 - To be honest, I'm not actually fussy on that logic of moving numbers or moving decimals as long as the child understands what's underlying logic that decimal applies to the number i.e. times 10 or divide by 10 when a decimal moves one place right or left.

No offence to anyone but I think that there's a serious gap in what state schools teach in Year 4/Year 5 compared to the level expected for top GS. For example see this question below:

9 pens and 5 pencils cost £3.20. 7 pens and 8 pencils cost £2.90.
The unit price for each pencil is _____ and pen is _______.

Parents - any ideas on what school would teach 10 yr old to solve this

Our school would not teach any child to solve this - not even top group year 6. Where did this question come from?

We got top group year 6 word problem homework last week. It was scarily basic. My job is not going to stop for a long while.

[SleepyHead]

9 pens and 5 pencils cost £3.20. 7 pens and 8 pencils cost £2.90.
The unit price for each pencil is _____ and pen is _______.

Interested to know how this can be explained to DD

Here is my method - anything simpler would be great!

So
9 pens and 5 pencils = 320p
7 pens and 8 pencils = 290p

therefore

2 pens minus 3 pencils = 30p

therefore by trial and error:
assume pencils are 10p each = 30p
so 2 pens must be 60 p
so 1 pen must be 30p

Check this works back with above

7 pens and 8 pencils = 290
7 * 30 and 8 * 10 = 290
210 and 80 = 290

therefore initial trial of pen = 30p and pencil = 10p worked

Any other method?
Thanks
Sleepyhead

[Proud_Dad]

9 pens and 5 pencils cost £3.20. 7 pens and 8 pencils cost £2.90.
The unit price for each pencil is _____ and pen is _______.

Interested to know how this can be explained to DD

Its a simultaneous equation.

9x + 5y = 320
7x + 8y = 290

The way we were taught to solve these at school was to mulitiply each equation by a factor so that one of the terms (x or y) becomes the same in each equation so they can then be combined or subtracted from each other to eliminate that term.

i.e.

multiplying the 1st equation by 8 and the second by 5 gives 40y in each equation:

72x + 40y = 2560
35x + 40y = 1450

Subtracting one of these from the other then gives

37x = 1110

Therefore x = 30.

Putting x = 30 into either of the original equations should then give you y.

i.e. (9 x 30) + 5y = 320

5y = 320 - 270 = 50

y = 10.

From what I remember though we learnt this in grammar school probably at around the old 3rd year (Year 9 in todays language), certainly not at primary school. Are people saying that questions like this will come up in the 11plus exam?

[parent2013]

Yes, it is simultaneous equation which could also be solved by hit n trial (if you're lucky)

Will it come in 11 plus?...... Only the staff designing the paper would know.

Has it come in the past? Yes, it has appeared for super selectives/private papers in one or the other form. So don't be surprised if it pops up.

However, I think it is too hard for Kent and CEM. My best guess is don't worry if you are targeting Kent and CEM.