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# Basic Algebra Fractions

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I'm having trouble with Fractions in Algebra and how to simplify them.

How would i simplify:

ab/ac

2e/4f

4a(sqared)b/2ab

a/b * b/c * c/a

(3x + 2)(squared) / 6x * x(power to 4) / 6x + 4

MathsGod1  Mar 28, 2015

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2*4= 8

2*7=12.       8+12=20

I don't understand. After adding the brackets on the last one you expanded it out but you added 2..?

MathsGod1  Mar 29, 2015
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I will use LaTex to help with the display. :)

$$\frac{15}{10}=\frac{3*5}{2*5}=\frac{3}{2}$$

Yes, I know, you already know that :)

You are allowed to do the same things with letters (pronumerals) as you can with numbers - so just follow the same rules.  :)

$$\\\(1)\;\;\frac{ab}{ac}=\frac{a*b}{a*c}=\frac{b}{c}\qquadThe a's cancelled out\\\\\\ (2)\;\;\frac{2e}{4f}=\frac{2*e}{2*2*f}=\frac{e}{2f}\qquadThe 2's cancelled out\\\\\\ (3)\;\;\frac{4a^2b}{2ab}=\frac{\not{4}^2*\not{a}*a*\not{b}}{\not{2}*\not{a}*\not{b}}=\frac{2a}{1}=2a \qquadThe rest cancelled out\\\\\\ (4)\;\;\frac{a}{b}*\frac{b}{c}*\frac{c}{a}=\frac{a*b*c}{b*c*a}=\frac{1}{1}=1\qquadThey all cancelled out\\\\\\ (5)\;\;\frac{(3x+2)^2}{6x}*\frac{x^4}{(6x+4)}\\\\ =\frac{(3x+2)*(3x+2)}{6x}*\frac{x*x*x*x}{2(3x+2)}\\\\ =\frac{(3x+2)}{6x}*\frac{x*x*x*x}{2}\qquadthe (3x+2)'s cancelled out\\\\ =\frac{(3x+2)}{6}*\frac{x*x*x}{2}\qquadan x cancelled out\\\\ =\frac{(3x+2)*x*x*x}{6*2}\\\\ =\frac{(3x+2)x^3}{12}$$

Melody  Mar 29, 2015
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So is it just to do with cancelling out?

MathsGod1  Mar 29, 2015
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Now that I've looked at it for a few minutes i can understand it very clearly.

For number 5, you've just cancelled the brackets the x from the 6 and from the x (power to 4) .

But one thing i don't get is, when you brought them together to get 6*2 = 12.

Was it possible to times the brackets with X(3)?

If not why?

Thanks.

(Really helped)

MathsGod1  Mar 29, 2015
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I have 2 questions about question 5.

When you factorised 6x+4 to 2(3x+2)

How did you know to factories there?

And when you brought them together how did you know when to, couldn't you have done it earlier?

Sorry for all the questions.

Hah I'm just very curious!

Thanks!

MathsGod1  Mar 29, 2015
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well you could go one more step

$$\\\frac{(3x+2)x^3}{12}\\\\ =\frac{x^3(3x+2)}{12}\\\\ =\frac{3x^4+2x^3}{12}\\\\$$

Does that help?

Melody  Mar 29, 2015
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okay lets look at factoring algebra 6x+4

----------------------------------------

do you know this

have you done it at school yet?

3(3x+2) = 3*3x+3*2 = 9x+6

Melody  Mar 29, 2015
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Kinda, I wanted to know how you knew when to bring them together and the factories  bit.

Also, the what you just did, did you put the x in front of brackets to be able to Times everything inside by the x?

MathsGod1  Mar 29, 2015
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No I haven't done factorising at all at school.

MathsGod1  Mar 29, 2015
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Study this and see if you can work out what I am trying to show you :)

they are all the area of rectangles.

Melody  Mar 29, 2015
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2*4= 8

2*7=12.       8+12=20

I don't understand. After adding the brackets on the last one you expanded it out but you added 2..?

MathsGod1  Mar 29, 2015
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No I didn't.

I will just talk about the last one.

One rectangle side is  2 units and the other is (4+y) units

y just stands for any unknown number if the y were 6 then it would be identical to the 2nd one.

Now the area of a rectangle is length * bredth = 2*(4+y) = 2(4+y)  the times can be invisable. :)

BUT

If you split this into 2 rectangles like on the picture then the areas are  2*4 and 2*y

SO

2(4+y)  MUST BE EQUAL TO  2*4 + 2*y

Think about it.  It takes a little time to absorb these new concepts :)

Melody  Mar 29, 2015
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Yes, when expanding the brackets the number outside will times everything on the inside but showing brackets just makes it easier instead of loads of *

MathsGod1  Mar 29, 2015
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im also confused with turning fractions to single fractions

1/a - 1/b + 1/c

MathsGod1  Mar 29, 2015
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You cannot learn every thing at once MG :)

Letters just stand for numbers so they behave exactly the same way.

$$\\\mbox{Hopefully you already know how to add fractions}\\\\ \frac{2}{3}+\frac{4}{5}\\\\ =\frac{2*5}{3*5}+\frac{4*3}{5*3}\\\\ =\frac{10}{15}+\frac{12}{15}\\\\ =\frac{10+12}{15}\\\\ =\frac{22}{15}\\\\\\ \mbox{Now add pronumerals (letters) the same way}\\\\ \frac{2}{a}+\frac{4}{b}\\\\ =\frac{2*b}{a*b}+\frac{4*a}{b*a}\\\\ =\frac{2b}{a*b}+\frac{4a}{a*b}\\\\ =\frac{2b+4a}{ab}\\\\$$

Melody  Mar 29, 2015
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No I didn't learn that at school.

But I have a simple idea of it and now I understand it.

Could I have a question on it please?

:)

MathsGod1  Mar 29, 2015
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Ok MG :)

What is

$$\frac{7}{12}+\frac{5}{9}$$

You need to find a common denominator first.  Something that 12 and 9 both go into.  You could use 12*9 which is 108, that would work but there is a smaller number that would be easier to use.

Can you work out what it is?  Can you answer the question?

Melody  Mar 30, 2015
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The smallest denominator is 3.

$${\frac{{\mathtt{7}}}{{\mathtt{12}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}}$$

$$\mathrm{ERROR} = {\frac{{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{4}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{3}}}{{\mathtt{9}}}}{\mathtt{\,\times\,}}{\mathtt{4}}$$

Umm...I had done what you done with your example on Math Formula and this came up.

And also when you done 3 & 5, 15 was bigger than both so you could times it by 5 & 3 but to times 12 and 9 by something to get 3. Would be a decimal.

MathsGod1  Mar 30, 2015
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You have used the highest common factor MathsGod1.

To get the smallest common denominator of 12 and 9 do the following:

Multiples of 9:    9   18   27   36  ...

Multiples of 12:  12  24  36 ...

So 36 is the smallest common denominator of 12 and 9.

.

Alan  Mar 30, 2015
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Silly mistake.

Thanks Alan

MathsGod1  Mar 30, 2015
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$${\frac{{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{3}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{4}}}{{\mathtt{9}}}}{\mathtt{\,\times\,}}{\mathtt{4}}$$

This is what i wrote 7*3/12*3 + 5*4/9*4 and i got that...

MathsGod1  Mar 30, 2015
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$${\frac{{\mathtt{21}}}{{\mathtt{36}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{20}}}{{\mathtt{36}}}}$$

$${\mathtt{21}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{20}}}{{\mathtt{36}}}}$$

i typed in 21+20/36 and got that. (which i don't want i want the 21 also on the numerator.

21+20=41

41/36

MathsGod1  Mar 30, 2015
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Note....if you wanted to  add   21/36  + 20/36  in one step.....use parentheses like this.....

(21 + 20) / 36   =  41/36

CPhill  Mar 30, 2015
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Yes good work MG - don't forget those brackets, they are really important :)

Melody  Mar 30, 2015
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Thanks CPhill and Melody.

I will remember the brackets :)

MathsGod1  Mar 30, 2015
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So...

Now what?

MathsGod1  Mar 31, 2015
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okay try this    (and see is you can write your answer in LaTex       )

HINT: Put plus signs between the whole numbers and the fractions, add the whole numbers first   :)

$$3\frac{2}{5}+6\frac{3}{4}$$

Melody  Mar 31, 2015
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$${\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}} = {\mathtt{9}}$$

$$2/5+3/4$$

5, 10, 15, 20, 25...

4, 8, 12, 16, 20, 24...

$$2*5/4*5 + 3*4/4*5$$

=  $$10/20 + 12/20$$

=$$10+12/20$$

$$22/20$$

Simpified =11/10

MathsGod1  Mar 31, 2015
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Great work MG.

You final answer can be changed into a mixed numeral. :)

It was really good to see you try LaTex but if you are going to use the / sign you must use brackets.

You have written

2*5/4*5+3*4/4*5

simplified this means

$$\\=\frac{2*5}{4}*5+\frac{3*4}{4}*5\\\\ =\frac{2*5}{4}*\frac{5}{1}+\frac{3*4}{4}*\frac{5}{1}\\\\ =\frac{2*5*5}{4}+\frac{3*4*5}{4}\\\\ =\frac{50}{4}+\frac{60}{4}\\\\ =\frac{110}{4}\\\\ =\frac{55}{2}\\\\ =27\frac{1}{2}$$

THIS IS OBVIOUSLY NOT WHAT YOU INTENDED

So this is how you needed to write it

(2*5)/(4*5)+(3*4)/(4*5)

which really does mean

$$\frac{2*5}{4*5}+\frac{3*4}{4*5}$$

This was my LaTex coding for these fractions. :)

\frac{2*5}{4*5}+\frac{3*4}{4*5}

---------------------------------------------------------

Here is some more - only do them if you want to.  :)

Hint:  Don't make a big deal out of these - they are quite simple.

$$\\1)\;\; 6-\frac{2}{3}\\\\ 2) \;\;12-3\frac{5}{9}\\\\$$

Melody  Apr 1, 2015
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did you actually type \frac{2*5}{4*5}+\frac{3*4}{4*5}?

1.     2/3 = $${\frac{{\mathtt{2}}}{{\mathtt{3}}}} = {\mathtt{0.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

6-(2/3)=$${\mathtt{6}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right) = {\frac{{\mathtt{16}}}{{\mathtt{3}}}} = {\mathtt{5.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$

2. $$12-3$$ = 9

12-5/9$${\mathtt{12}}{\mathtt{\,-\,}}{\frac{{\mathtt{5}}}{{\mathtt{9}}}} = {\frac{{\mathtt{103}}}{{\mathtt{9}}}} = {\mathtt{11.444\: \!444\: \!444\: \!444\: \!444\: \!4}}$$

Honestly, i have no idea what i done...

MathsGod1  Apr 1, 2015
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I want you to do them WITHOUT the calculator please MG

Here is some more - only do them if you want to.  :)

Hint:  Don't make a big deal out of these - they are quite simple.

$$\\1)\;\; 6-\frac{2}{3}\\\\ 2) \;\;12-3\frac{5}{9}\\\\$$

Melody  Apr 2, 2015

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