Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Common

Taking common in algebra helps to solve expressions.

Last edited by Zeeshan 01 (2018-06-22 15:08:48)

---

Malik

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Common

Try this:

http://www.mathsisfun.com/associative-c … utive.html

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Common

The first thing you should always do is try it.

3 x (2+5) does equal 3 x 2 + 3 x 5

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: Common

hi Zeeshan 01

Here is an example:

12 + 15

12 = 3 x 4
15 = 3 x 5

They have a common factor.  The common factor is 3.  Factors only apply to multiplication.  So 3 and 4 are factors of 12.  5+7 = 12 but 5 and 7 are not factors of 12.

So it is possible put the common factor outside a bracket, with the other factors added inside the bracket:

12 + 15 = (3 x 4) + (3 x 5) = 3 x (4+5)

This simple picture shows why it works.

You can do the same with algebraic expressions.

example.

4y + 6z = 2 times (2y) + 2 times (3z) = 2 times (2y+3z) = 2(2y+3z)

Note: When I first wrote the line above I used an 'x' to stand for times or multiply.  But it looked very confusing.  How will it look when letter 'x' is one of the algebraic symbols?  This is why it is usual to leave out the times signs in algebraic expressions.  Sometimes a dot . is used to show multiplication.  Thus:

We write 4y = 4.y when we mean 4 times y.

example.

x is a common factor so we can move it outside a bracket:

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: Common

I have edited my post above to make it clearer.  Have a look at the most recent version.

Is there anything else I can help with?

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: Common

You cannot see my rectangle?

Let's test with another page.  Is there a circle with lines drawn on this page:

http://www.mathisfunforum.com/viewtopic.php?id=22507

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