Mandy Jane's Corner

SteveB · 2013-03-20 06:00:47

By the way I would like to add an important point about basic arithmetic using fractions:

When adding fractions it is very important to always make the denominators (the bottom numbers) the same first.
(The same applies to subtraction.)

When multiplying however you can just multiply the numerators and denominators.

Last edited by SteveB (2013-05-09 07:01:58)

Mathegocart · 2013-03-20 10:56:41

Steve,what is she doing?
It looks like she is doing Fraction//percents/?
Here are some questions for practice Mandy.Steve if you are here,teach mandy
1. $9=?$

2. $8$

3. $8=?$

SteveB · 2013-03-21 02:15:58

mathgogocart wrote:

Steve,what is she doing?
It looks like she is doing Fraction//percents/?

Percentages ... but fractions were necessary for my explanation to make sense.
Every fraction can be written as a fraction with 100 as the denominator and is therefore a percentage.
So percentages can be converted into a fraction with 100 as the denominator (and cancelled if appropriate).

If you multiply by a percentage then it solves a problem in the form " A% of a number ".

You could re-write this as: (A %) x (number) = (A/100) x number = (A x number) / 100

Last edited by SteveB (2013-05-09 07:02:59)

mandy jane · 2013-03-21 02:56:44

[\math]\frac{1}{5} x \frac{3 }{7 } = \frac {3 }{23 }[\math]

[\math\]\frac {2}{3 } x \frac {4}{10} = \frac {8}{30} [\math]

[\math]\frac {3 }{5} x \frac {5}{3} = \frac {15}{15} [\math]

Last edited by mandy jane (2013-03-21 03:01:21)

SteveB · 2013-03-21 03:01:41

mandy jane wrote:

\frac{1}{5} x \frac{3 }{7 } = \frac {3 }{23 }

This one is incorrect. However I think it is just that you got the times table bit wrong. 5 x 7 is not 23. Try again perhaps?

\frac {2}{3 } x \frac {4}{10} = \frac {8}{30}

Yes that is correct. Do you know how to cancel the fraction down to a simpler form?

\frac {3 }{5} x \frac {5}{3} = \frac {15}{15}

Again that is correct. How could you cancel or simplify this ?

PS. if you use the frac thing in Latex you need to use the [math] tags as well.

PS no 2: If you are using Latex you need to start with [math] without the \ .... if you see what I mean.

Last edited by SteveB (2013-03-21 03:05:42)

mandy jane · 2013-03-21 03:12:30

Last edited by Bob (2013-03-21 03:47:03)

SteveB · 2013-03-21 03:14:07

Good you have got the hang of it. You can use \times to give an x
I know what you mean, but some people could argue that you have used 'x' in the sense of the letter here.

More importantly the denominator is still wrong.

5 x 7 is not 25 either.

Last edited by SteveB (2013-03-21 03:21:54)

mandy jane · 2013-03-21 03:16:36

I have. Done post 706 again ok?

SteveB · 2013-03-21 03:20:43

I have done my post again as well.

mandy jane · 2013-03-21 03:27:06

5 x 7 =35 am I right?

SteveB · 2013-03-21 03:28:07

The reason why I have given us another look at fractions is that any percentage can be re-written as a fraction
with 100 as the denominator and cancelled down if appropriate.

So let us say that the percentage is 50%

We can write this as:

Can you see how we could cancel or simplify this fraction ?

SteveB · 2013-03-21 03:29:52

I have just looked at post #710 and you are correct. Good. Now look at post #711.

mandy jane · 2013-03-21 03:33:44

50 goes into 100 2times and 50 goes into 50 1 so 1/2 am I right?

SteveB · 2013-03-21 03:35:13

Yes this is correct so let us consider a problem involving 50 %

I need to calculate 50 % of 70. How could I do this ?

SteveB · 2013-03-21 03:38:44

Okay I will give you a clue:

Substitute 50 % with (1/2) then multiply. The number 70 could be thought of as a fraction of (70/1)

Last edited by SteveB (2013-03-21 03:40:13)

mandy jane · 2013-03-21 03:40:44

not sure what to do?

SteveB · 2013-03-21 03:45:44

Right here is what I was trying to get you to work out:

You have worked out that 50% = (50/100) = (1/2)

We need 50 % of 70.

So this is the same as: (1/2) x 70

Which is: (1/2) x (70/1)

Using the fraction multiplication rules:

This is: (70/2)

In this case because the number 70 was a whole number we did not really need to convert it into a fraction,
but if we use fraction multiplication then you know how to multiply a fraction by a percentage as well.

SteveB · 2013-03-21 03:46:51

Now what can we cancel (70/2) to ? Is this a whole number ?

mandy jane · 2013-03-21 03:48:29

what do you think we should do now then?

SteveB · 2013-03-21 03:50:08

Have you got a calculator handy?

If so how about you type the division 70 divided by 2 into it. What do you get?

What does this tell you about the fraction (70/2) ?

mandy jane · 2013-03-21 03:53:53

70/2 can go down to 35/1 am i right?

SteveB · 2013-03-21 04:01:26

Just to re-cap:

50 % of 70 was the original question.

SteveB · 2013-03-21 04:04:50

Yes your post #721 is correct.

So this fraction (35/1) is actually a whole number. It is simply 35 because any number divided by 1 is the number itself.

So 35 divided by 1 is 35. So (35/1) = 35 also.

Right I will now give you a similar problem. See if you can work it out. What is 40% of 60 ?

mandy jane · 2013-03-21 04:05:36

not sure what to do next?

SteveB · 2013-03-21 04:08:52

Right let us look at the 40 % bit of that question. What can we re-write that as ?

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