-2/3 + -4/5=?

Question

-2/3 + -4/5=?    (These are fractions)

Answer 1

Firs of all.... DONT ADD THE TOP (numerators) TOGETHER and the BOTTOMS (denominators) TOGETHER..

 

Look at the fractions, since they have different denominators you must find the LCD (Least Common Denominator).  In order to do that, Find the multiples of both denominators and find the first number the have in common.. (if you don't know what a multiple is think of the multiplication tables).  Here we go:

 

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 you get the idea

5: 5, 10, 15, 20, 25, 30, 35 .....

 

What is the first number they have in common????? Yes, you are a GENIUS: 15.  Yes, they have 30 in common also, but this is not the LCD.  However, if you use the 30, you are also going to get the correct answer at the end.

 

Now that we found the LCD (first number they have in common.  I am going to set up two proportions.

 

(-2)/3 = x/15          and     (-4)/5 = y/15

 

 

1) to solve for x: multiply (-2)(15) and (3)(x).  These are called CROSS PRODUCTS.  So, you end up with

 

-30= 3x,  divide both sides by the COEFFICIENT of x, this becomes X= -10

 

so, (-2)/3 = -10/15

 

2) to solve for y: multiply (-4)(15) and (5)(x). So, -60=5x.  divide both sides by 5. You end up with y=-12. Therefore,  (-4)/5= -12/15

 

Now take a look at the original problem:

 

-2/3 + (-4/5):  This is what you end up with:  (-10/15)+ (-12/15).  Since now both equations have the same denominator.  Add the numbers on the top (NUMERATORS) and KEEP the same number on the bottom (denominators)

 

What we end up with is:  -32/ 15: This is an IMPROPER FRACTION, so, we need to this into a whole number or a MIXED NUMBER.  If we do that, we end up with -2 2/15.  Negative 2 and 2/15.

 

I hope this helps you out.