Math Is Fun Forum

First of all what is the basic pay for the week ?

Firstly it does not really matter if you get a decimal and second you do not necessarily have to be concerned about whether the
number/ratio you are trying to transform is smaller or larger.

On the other hand whole numbers are nice to work with and it may be easier to try to get a result which only has whole numbered
components. In this case you are scaling the thing down as I understand it so there is perhaps a greater chance of ending up with
a number which requires digits after the decimal point. (It is a fact of life that numbers requiring a decimal point are more common.)

Here is an example of a ratio conversion that converts a higher set of numbers to a lower set with whole numbers only:

3 : 6 : 9   is the same as  1 : 2 : 3  (here I have divided each element of the ratio by 3 I could have multiplied by one third)

(obviously that example does not have the same ratio as your problem)

If the second ratio contained only two elements and I wanted to find the third then it can only be done if the two I have given are
in the correct ratio. If I chose 4 : 7 : ? then that would not be possible for 3 : 6 : 9 however if I change the 7 to an 8 then we get
4 : 8 : 12

In your example in the earlier post the problem is that the two numbers you gave for the new ratio are already incorrect relative
to each other. In other words one must be changed. Either the original measurements are wrong or the two numbers in the
second ratio are not in the right ratio relative to each other. The fact that the second number is larger than the first, but the other
way round in the other ratio immediately alerts a mathematician to an inconsistent proportion.

If I have the ratio 3 : 6 : 9 and I want a model to be 1 : 7 : ???  then the first number has to go from 3 to 1, but the second has
to go from 6 to 7, with the same multiplication. Well this is not going to work because 3 multiplied by a third equals 1
but if I do the same multiplication to the second number 6 get transformed to 2. One cannot go up and the other down.
In fact the two numbers that we give for the second ratio have to be in the correct ratio of the first two numbers of the first ratio.
It would probably by a good idea to look at Bob's post including the image file he posted (if you haven't already done so).
Trying to explain this using plain text only is not easy and could cause confusion.

Anyway I hope that has cleared the matter up rather than muddied the waters even further.

If 1012 was the dividend and 11 the divisor then it is certainly 1012 divided by 11 not the other way round.

11 divided by 1012 is a very difficult division to do if you are new to long division.
Long division is actually very similar to short division, the only real difference is that in long division you display the multiples
of the divisor clearly in the division as well as the remainders. If you try the division using short division you will actually see
that the remainders at each stage are the same. Bob is correct with the remainders, but extremely strictly speaking it is not
quite right because the first two rather trivial stages in which a zero is obtained in the division have been left out.

Strictly speaking you should first try to do 1 divided by 11 which is zero remainder 1. The zero from the result is a put up the
top in the answer part and a zero is put below the 1. Then a zero is dropped down and the 1 will now have the appearance of
a ten (if you think about it 1 thousand is equal to 10 hundreds). Then we try to do 10 divided by 11. The result is zero with
a remainder of 10 (10 - 0 = 10). Then drop another number down which is a 1. The ten is in effect promoted by a factor of
ten to 100 because ten hundreds is the same as 100 tens and the dropped down 1 makes it 101. Then we do 101 divided by 11.
This is a bit more interesting.

Here we go into the bit that Bob has done with the use of the fact that 9 x 11 = 99 so therefore 101 divided by 11 gives us
9 (the number of times 11 goes into the number) and a remainder of 2.   
9 is put in the answer at the top.
The 2 is 2 tens and this is 20 units when we drop down the next digit which is 2 we get 22.   
22 divided by 11 is 2.
The result is that we have an exact answer. So no need for decimals here. If a remainder results at the end then you can
add a decimal place and continue dropping down zeros (that is another story). Here because we have an exact answer and
all of the non trivial numbers have been dealt with the answer is given.
I have decided to include my version of this for completeness, but it is very similar to Bob's diagram. The only real difference
is the rather trivial bit at the beginning where we get zero multiples of 11 and just drop another digit of 1012 down.

Good question. I could give you another overtime question if you feel that you need more practice.
You did struggle with that one so I probably ought to.
Also I do not at the moment know what it is to do with time that you are supposed to be learning about.
The thing that springs to mind is something like how many seconds there are in a day or something.
Do you want another question on overtime now ? Or would you prefer to move on to time ? (If you want to do time
then I need to know what sort of question you need to know about how to do)

Correct. Well done.

Have you any ideas about what to do next ?

No that is not correct the £5.25 needs to be added on to £7.00

Then multiply it by 2 because there were 2 hours worked on Sunday.

I think what you did there was to add on a third of £7.00 to 1 decimal place and to add it three times.

In fact you should have divided by 4 so you get 1.75 then multiply by 3, and then add it on.

Do you want to try again ?

Yes that is correct. Now how about the Saturday rate what is that ?  (time and a half)

Okay. The basic hours bit of it I am sure you can do because that is just 35 x 7

Right now I have said "time and a quarter" for the Friday overtime. The number of hours was 5
The basic rate of pay was £ 7.00
Once again there are different ways you can approach the problem, but they all amount to the same thing:
I would be inclined to work out a rate of pay for this overtime. So do £7.00 / 4
Then add this to £7.00

£ 7.00 - hourly rate
35 hours - normal full time hours

Monday to Friday overtime: time and a quarter
Saturday overtime: time and a half
Sunday overtime: the basic rate plus 3 quarters

The employee does the 35 basic hours plus:
5 hours extra on a Friday
and 4 hours on Saturday,
and 2 hours on Sunday

Calculate the basic pay,
overtime pay on Friday,
the overtime pay for Saturday,
and the overtime pay for Sunday
Add them together to get a total.

Is is that one you are trying to do?

With the Saturday bit of the overtime here are three ways that you could do this:

£ 7.50 x 2 hours = £ 15.00 (at basic rate)
Since the overtime is at time and a half:
£ 15.00 / 2 = 7.50
£ 15.00 + £ 7.50 = £ 22.50 (at Saturday overtime rate)

OR

£ 7.50 / 2 = £ 3.75
£ 7.50 + £ 3.75 = £ 11.25
£ 11.25 x 2 hours = £ 22.50

OR if calculators are allowed

£ 7.50 x 1.5 x 2 hours = £ 22.50  (the 1.5 bit is to allow for the "time and a half" rate)

Okay. Bye for now.