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## #1 2019-11-15 05:09:01

LegionXII
Member
Registered: 2019-11-15
Posts: 2

### Explanation for Multiplying/Dividing in Equations/Inequalities

I'm studying maths again after nearly a 7 year break from it and while I'm doing well (better than I ever have in school, matter of fact) there are still a couple of things that I haven't been completely explained; namely, the rules when multiplying/dividing in equations.  While I know what the rules are, I still haven't been explained WHY it differs from adding and subtracting.  For instance:

Say I have the equation 4x+(3/4)-1=5+20

If I want to get rid of the fraction (3/4) I have to multiply 4 by the entire equation on both sides:

4(4x+(3/4)-1)=(5+20)4

The same goes for division.  But.. when adding or subtracting, instead of it being, say when adding 1 to both sides:

4x+(3/4+1)-(1+1)=(5+1)+(20+1) it's simply 4x+(3/4)-1+1=5+20+1

Why is that?

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## #2 2019-11-15 15:51:42

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

### Re: Explanation for Multiplying/Dividing in Equations/Inequalities

A=4x+(3/4)-1
B=5+20
A = B
thus
kA = kB
A/k = N/k as long as k<>0
A+k = B+k

X'(y-Xβ)=0

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## #3 2019-11-15 21:05:51

Bob
Registered: 2010-06-20
Posts: 9,903

### Re: Explanation for Multiplying/Dividing in Equations/Inequalities

hi LegionXII

Welcome to the forum.

The rules for algebra are just the same rules that are used for arithmetic.  If ever you are uncertain about some algebra just try a similar thing with numbers.  Here's a couple of examples to show what I mean:

If I multiply just one term on the left and one on the right by 4,  I'll get

As you can see this is NOT correct.

You must multiply every thing by 4

Now we have a correct result.

Both sides are now 9/4 so it is correct to do it this way.

The two rules that are being used here are:

(1) If we have a correct equation it will still be correct if we multiply every term on each side by a number.

(2) If we have a correct equation it will still be correct if we add the same amount to each side.

Hope that helps.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #4 2019-11-16 03:01:48

LegionXII
Member
Registered: 2019-11-15
Posts: 2

### Re: Explanation for Multiplying/Dividing in Equations/Inequalities

Ah thank you, this definitely helps to clear it up.

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