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Here is another set of fractions, decimals and percentages, I will send you a spreadsheet version of these:

Fraction Decimal Percentage

1/5

1/8

3/20

2/25

0.5

0.35

0.75

55%

95%

24%

4/5 0.8 80.00%

1/12 0.0833 8.33%

6/7 0.8571 85.71%

1/3 0.3333 33.33%

13/20 0.65 65.00%

4/25 0.16 16.00%

11/20 0.55 55.00%

3/5 0.6 60.00%

2/5 0.4 40.00%

1/5 0.2 20.00%

4/5 0.8 80.00%

1/2 0.5 50%

1/4 0.25 25%

2/5 0.4 40%

3/20 0.15 15%

9/20 0.45 45%

3/4 0.75 75%

5/8 0.625 62.50%

3/8 0.375 37.50%

49/50 0.98 98%

7/40 0.175 17.50%

3/8 0.375 37.50%

3/5 0.6 60%

11/25 0.44 44%

3/25 0.12 12%

1 1 100%

The correct answer is in fact (3/25) as a fraction and not (6/25) so sorry about that.

The working for this might go as follows:

0.12 = 12 /100

12 /100 = 6 / 50

6 / 50 = 3 / 25

I wrote those out in a hurry.

The latest set of questions are as follows:

Fraction Decimal Percentage

4/5 --------- -----------

1/12 --------- -----------

6/7 --------- -----------

1/3 --------- -----------

---------- 0.65 -----------

---------- 0.16 -----------

---------- 0.55 -----------

---------- ---------- 60%

---------- ---------- 40%

---------- ---------- 20%

---------- ---------- 80%

My apologies by the way about 1/12, 6/7 and 1/3

I realise that these need rounding.

I should try to round them to 2 decimal places if you can.

See if you can format the text in the spreadsheet,

but don't worry if you can't.

I can't insert the fraction, decimal and percentage work as an image however here is a plain text version of the latest set of practice questions for you. Each series of minus signs represents an item for you to try and work out.

Fraction Decimal Percentage

1/2 ---------- ------------

------- 0.25 ------------

3/20 ---------- ------------

-------- 0.45 75%

5/8 ----------- ------------

-------- 0.375 ------------

-------- ----------- 98%

7/40 ------------ ------------

------- 0.675 ------------

------- ------------ 60%

22/50 ------------ ------------

------- 0.12 ------------

------- ------------ 100%

Question (1) Consider the following 10 symbols : XXXOOOOOOO

There are 3 Xs and 7 Os

What percentage are Xs ?

What percentage are Os ?

Draw a diagram with 100 items if it helps.

Question (2) Consider the following diagram:

OOOOOXXXXX

OOOOOXXXXX

OOOOOXXXXX

OOOOOXXXXX

OOOOOXXXXX

There are 50 symbols in total. Imagine that there were twice as many and in the same proportion.

What percentage are Os ?

What percentage are Xs ?

Question (3)

Draw a diagram that represents 25% Xs and 75% Os

The total number of symbols must be 8.

Question (4)

Draw a diagram in which 40% are Xs and 60% are Os.

The total number of symbols must be 20.

I will send you an email copy of that lot just in case it is easier to see in an email.

How about this for instance XXXOOOOOOO

There are 3 Xs and 7 Os there.

What percentage are Xs and what percentage are Os ?

The point is: Do you now understand percentages or do we need to give you some more questions to test your understanding? I would say that we do.

With question 3 you did not manage to end up with a representation so no marks for that I'm afraid.

With question 4 you would only be right if there were another 96 symbols knocking about somewhere so I will class that as a good effort, but wrong.

So 2 out of 4 correct.

Question 3 was probably the most tricky for you,

but if you think about it if you have

"Using only 4 symbols in total represent 25% Xs and 75% Os"

then we want to end up with 4 symbols in total.

So what is 25% of 4 items? Well the answer is 0.25 x 4 = 1

So we have only 1 X

Now what is 75% of 4 items? Well the answer is 0.75 x 4 = 3

So we have only 3 Os

So the answer is XOOO

Let us have a look at question 4 and think about it in a different way:

We had 4 symbols in total namely:

XX

OO

Now let us imagine that we repeat those four items until there are 100 symbols:

XXOO XXOO XX

OO XXOO XXOO

XXOO XXOO XX

OO XXOO XXOO

XXOO XXOO XX

OO XXOO XXOO

XXOO XXOO XX

OO XXOO XXOO

XX OOXX OOXX

OO XXOO XXOO

There are 100 symbols altogether.

There are 25 pairs of Xs so there are 50 Xs.

There are 25 pairs of Os so there are 50 Os.

I conclude that 50% are Xs and 50% are Os.

The answer obtained by 3/9 would be 33.333.... % which is not right.

The denominator (bottom of the fraction) is the whole of them.

The numerator (top of fraction) is the "partial bit" of the proportion in each case.

Try again ?

Reminder of the question:

Let us call this Question (1):

What are the percentages in this case:

OOO

XXX

XXX

XXX

What percentage of those are Os ? What percentage of those are Xs ?

ANSWER: 25% are Os and 75% are Xs.

I was wanting to see something like this:

total number of items = 12

3/12 = 0.25

9/12 = 0.75

0.25 = 25%

0.75 = 75%

EDIT: Please refer back to post number #1429 at the end of the post.

Another question:

Let us call this Question (2):

What percentage of these are Xs ?

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

Each row has exactly ten items in and the total is 100.

ANSWER:

Since the total is already 100 by inspection 30% are Xs and 70% are Os

Here are four questions on percentages for you:

Question (1)

Using 100 symbols in total which are either Xs or Os represent the percentage 40% Xs and 60% Os

Question (2)

What are the percentages of Xs and Os in this diagram?

XXXXXXXXXX

XXXXXXXXXX

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

Question (3)

Using only 4 symbols in total represent 25% Xs and 75% Os

Question (4)

What percentages of Xs and Os are represented by this diagram?

XX

OO

The total of all of them is 12 so the thing on the lower part of the fraction has to be the amount that it is out of.

You could try expressing it as a fraction first that would be my method as well.

Let's revise percentages. Don't worry about those above questions Mandy.

Here are a few examples of O and X percentages where the number of letters rather than the area is of concern.

Since the letters have different widths I will stick to the same length of row in each case in terms of the letters.

This is a case of 10% Xs and 90% O

XXXXXXXXXX

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

Of course since percentages are a measure of proportion there don't have to be 100 items as such:

X

OOOOOOOOO

If you have the above situation then there are 9 Os and 1X there so the proportion of Xs is still 10%

and the proportion of Os is still 90%

If you have this:

OO

XX

The proportions are 50% X and 50% O

You could expand this to:

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

So there are 5 lots of ten of each. So there are 50 Os and 50 Xs meaning 50% O and 50% X.

I will leave it there for now. You have some reading to catch up on. I will leave you to it.

One question for you to try:

What are the percentages in this case:

OOO

XXX

XXX

XXX

What percentage of those are Os ? What percentage of those are Xs ?

EDIT: Another hint:

OOOOOOOOOO

OOOOOOOOOO

OOOOOXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

Mandy. Are you okay? Are you still continuing this?

Perhaps continue on Monday?

EDIT:

Consider a series of Os and Xs:

OOOOOOOOOO

OOOOOOOOOO

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

Each row has 10 of the letter. Two fifths of these are Os and three fifths are Xs.

Imagine that there were two lots of that ie:

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

XXXXXXXXXX

Out of 100 there are 40 Os and 60 Xs. So as a percentage there are 40% Os and 60% Xs.

You could do 2/5 = 0.40 then x 100 -> 40 %

and then 3/5 = 0.6 then x 100 -> 60 %

Now try answering Q4 with that method and round the answer off.

Okay I will reveal the answer to Q4:

I am getting: 9/29 = 0.31034... = 31.034...%

Rounded to the nearest percentage 31%

I am getting 7.5 / 29 = 0.258620..... = 26% rounded to the nearest percentage.

I will go through the other questions for completeness....

I apologise in advance if there are any mistakes.

The rate part of the question involves a cost of £3 per cubic metre and 120 cubic metres used.

So we do: £3 x 120 = £360

The standing charge added on is £100 regardless of other costs so:

£360 + £100 = £460

Then an allowance for VAT at 20% has to be made so:

£460 x 1.20 = £552

First observe that 13000 kWh has been used and divide by 1000.

This is because the rate is 47.50 per 1000 kWh.

So we do £47.50 x 13000 / 1000 = £617.50

Then add the yearly standing charge of 150:

£617.50 + £150 = £767.50

Then add 20% VAT:

£767.50 x 1.2 = £921

I am getting (37 x £7) + ( 2 x £9 ) = £277

I am getting £259 x 4 = £1036

£277 x 48 = £13296 for the amount excluding holiday pay

£13296 + £1036 = £14332

£4332 is taxable

£4332 x 0.2 = £866.40

Okay I agree let us leave it a day.

EDIT:

Answer to Q3 for the record: 212.62125/500 = 0.4252425

Multiply by 100 to convert to a percentage: 42.52425% which rounds to 43%

Since Q4 is slightly easier than Q3 and similar you might like to attempt Q4.

I will leave it up to you. Take your time and try to get the answer correct.

Yes that's correct.

Hint: What is the numerator and what is the denominator? What has to be divided by what?

Do you have to multiply by 100 for any reason?