Thread: Grade 9 Equations with Fractions

Hi all.
I have an ext. exam coming up tomorrow and I needed help with Equations with Fractions.
I looked up a tutorial and got this, which I do not understand:

x 3

+

x − 2 5

= 6

Multiply both sides of the equation -- every term -- by the LCMof denominators. Every denominator will then cancel. We will then have an equation without fractions.

The LCM of 3 and 5 is 15. Therefore, multiply every term on both sides by 15:

15·

x 3

+

15·

x − 2 5

= 15· 6

Each denominator will now cancel into 15 -- that is the point -- and we have the following simple equation that has been "cleared" of fractions:

5x + 3(x − 2)

=

90.

How do they multiply the terms by 15?
Like how do they multiply 15 by x over 3?
This is confusing. :P

Thanks in advance!

Originally Posted by JesseElFantasma

Like how do they multiply 15 by x over 3?

I don't understand your question. What do you mean by "how"? One is allowed to multiply any number by any other number; multiplication is defined for every two numbers. Do you mean "How to simplify "? Do you mean "Why "? Do you mean "Why is equivalent to "? What exactly is your question?

Originally Posted by emakarov

I don't understand your question. What do you mean by "how"? One is allowed to multiply any number by any other number; multiplication is defined for every two numbers. Do you mean "How to simplify "? Do you mean "Why "? Do you mean "Why is equivalent to "? What exactly is your question?

Yes, why does 15 multiplied by x over 3 equal 5x ?

Originally Posted by JesseElFantasma

Yes, why does 15 multiplied by x over 3 equal 5x ?

Do you know how to divide 15 by 3?

It may be more convenient to break division into two operations: multiplication and reciprocal function. Thus, x / y would really mean x * (1 / y). This is, in fact, how it is done in higher mathematics.

As you know, multiplication obeys the following laws:

x * y = y * x (commutativity)
x * (y * z) = (x * y) * z (associativity)

Therefore,

= 15 * (x / 3) =
15 * (x * (1 / 3)) = (by definition of division)
15 * ((1 / 3) * x) = (by commutativity)
(15 * (1 / 3)) * x = (by associativity)
5 * x

because 15 * (1 / 3) = 15 / 3 = 5.

Think of as a brick, (or some other object if you prefer it).

divided by means that the brick is being divided into three pieces, is a third of a brick.

Now suppose that you have of these and that they could be stuck back together again. How many whole bricks could you make ?

Answer bricks. Algebraically,

For the next term, relate to some object.