Why should we clear fractions when solving linear wquations and inequalities? De

Question

Why should we clear fractions when solving linear wquations and inequalities? Demonstrate how this is done with an example. Why should we clear decimals when solving linear euations and inequalities? Demonstrate how this is done with an example.

Explanation / Answer

It just makes things easier in general. Take fractions for example: if you have y/2 = 3x/4 + 16/6 -> the lowest common denominator is 12, because 12 is the lowest number that will clear all the fractions, so: 12 (y/2 = 3x/4 + 16/6) 6y = 9x + 32 -> of course, if you want to graph this linear equation, you need to solve for y, so you would have to divide the whole equation by 6. (6y = 9x + 32)/6 y = 9x/6 + 32/6 -> simplify the fractions y = 3x/2 + 16/3 -> this is your equation for y. For decimals it's not much of a difference but it still makes it easier... for example 2.1x + 0.65x = 55 we could add to get 2.75x = 55 and then divide by 2.75 or... we can clear the decimals by multiplying by 100 100(2.1x + 0.65x = 55) => 210x + 65x = 5500 add together the first two terms and then divide... 275x = 5500..... 5500/275 = x = 20 Either way you do it, it'll still be the same answer, just this way you can do it in your head quicker...

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