Algebra Period 4

Clearing An Equation of Fractions or Decimals 3-6

You can do equations with fractions or decimals as they are, but many 
students find it easier to "get rid of" them!


How? Just use the multiplicative property of equality! (your old friend!)


DECIMALS:
16.3 - 7.2y = -8.18

Multiply by the power of 10 needed to clear ALL decimals!

In the problem above, you would need to multiply by 100 to make -8.18 an integer

100 (16.3 - 7.2y) = 100 (-8.18)

USE THE DISTRIBUTIVE PROPERTY ON THE LEFT SIDE OF THE EQUATION

1630 - 720y = -818

SUBTRACT 1630 FROM EACH SIDE (or add -1630)

1630 - 1630 -720y = -818 - 1630

-720y = -2448

DIVIDE EACH SIDE BY -720

-720y/-720 = -2448/-720

y = 3.4

ALWAYS CHECK YOUR ANSWER!!!!!


Why do students get this wrong?
1)
1) They forget to multiply the integers by the power of 10 because it doesn't have any decimal places to "get rid of".
Remember: to stay in balance, you must distribute to EVERY term.
2) They distribute only the power of 10 that each term needs. 

For example, if the problem has .3y = 2.85, you will need to multiply by 100 EQUALLY on both sides to stay in balance, but students will end up with 3y = 285.

THIS IS WRONG!!!
YOU HAVE MULTIPLIED BY 10 ON LEFT SIDE AND 100 ON RIGHT SIDE!
YOU ARE OUT OF BALANCE!!!



FRACTIONS:
Are you "Fraction Phobic"????

Then you're going to love this!!! :)


2/3y + 1/2y = 5/6 + 2y

Instead of finding a common denominator and using fractions, we're going to...

MULTIPLY BY THE LCM OF ALL THE DENOMINATORS

In the problem above, the LCM of 3, 2, and 6 is 6

6 (2/3y + 1/2y) = 6 (5/6 + 2y)

USE THE DISTRIBUTIVE PROPERTY ON BOTH SIDES OF THE EQUATION

6(2/3y) + 6(1/2y) = 6(5/6) + 6(2y)

4y + 3y = 5 + 12y

COMBINE LIKE TERMS ON THE LEFT SIDE OF THE EQUATION

7y = 5 + 12y

SUBTRACT 12y FROM BOTH SIDES TO GET ALL VARIABLES ON ONE SIDE

7y - 12y = 5 + 12y - 12y

-5y = 5

DIVIDE BOTH SIDES BY -5

-5y/-5 = 5/-5

y = -1

ALWAYS CHECK YOUR ANSWER!!!!!


Why do students get this wrong?
1)They forget to multiply the integers by the LCM because it doesn't have any denominator to "get rid of".
Remember: to stay in balance, you must distribute to EVERY term.

2) They distribute only the number that each denominator needs. Again, you're out of balance.

3) They multiply by the wrong LCM...you'll end up still having a denominator.
You have not achieved your objective under this method! Your objective is to get rid of every denominator!



Couldn't I just solve these problems keeping the decimals and fractions?

Yes, you could, but I want you to learn this method because you might like it!


Also, you will to know how to get rid of the denominators in Chapter 10 when you have very complicated denominators with variables.