# Math Help - Grade 9 Equations with Fractions

1. ## 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

2. ## Re: Grade 9 Equations with Fractions

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 $15\frac{x}{3}$"? Do you mean "Why $15\frac{x}{3}=5x$"? Do you mean "Why is $\frac{x}{3}+\frac{x-2}{5}=6$ equivalent to $15\frac{x}{3}+15\frac{x-2}{5}=15\cdot6$"? What exactly is your question?

3. ## Re: Grade 9 Equations with Fractions

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 $15\frac{x}{3}$"? Do you mean "Why $15\frac{x}{3}=5x$"? Do you mean "Why is $\frac{x}{3}+\frac{x-2}{5}=6$ equivalent to $15\frac{x}{3}+15\frac{x-2}{5}=15\cdot6$"? What exactly is your question?
Yes, why does 15 multiplied by x over 3 equal 5x ?

4. ## Re: Grade 9 Equations with Fractions

Originally Posted by JesseElFantasma
Yes, why does 15 multiplied by x over 3 equal 5x ?
Do you know how to divide 15 by 3?

$15\cdot\frac x3$

$=\frac{15}1\cdot\frac x3$

$=\frac{15\cdot x}{1\cdot3}$

$=\frac{15x}3$

$=\frac{5x}1 = 5x$

5. ## Re: Grade 9 Equations with Fractions

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,

$15\frac{x}{3}$ = 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.

6. ## Re: Grade 9 Equations with Fractions

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

$x$ divided by $3$ means that the brick is being divided into three pieces, $\frac{x}{3}$ is a third of a brick.

Now suppose that you have $15$ of these and that they could be stuck back together again. How many whole bricks could you make ?

Answer $5$ bricks. Algebraically, $5x.$

For the next term, relate $(x-2)$ to some object.