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is -10/3/4 greater than or less than -41/5

 Sep 14, 2017
 #1
avatar+5258 
+1

-10 3/4 < or > -41/5

 

First, let's change the mixed number to a single fraction.

 

-10*4+3

 

-43/4 is the improper fraction we're gonna have

 

Now, let's find the LCD (least common denominator)

 

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

4,8,12,16,20,24,28...

 

The least common denominator is 20

 

To get -43/4 to __/20, multiply -43 and 4 by 5

 

-43*5=-215

4*5=20

 

To get -41/5 to __/20, multiply -41 and 5 by 4

 

-41*4=-164

5*4=20

 

Our fractions now are 

 

-215/20 < or > -164/20

 

Remember that with negatives, the larger number is less than the smaller number

 

-215/20 < -164/20

 

-10 3/4 < -41/5 

 

In words, negative ten and three quarters is less than negative forty-one fifths.

 Sep 14, 2017
 #2
avatar+98090 
+2

Thanks, rarinstraw !!!!

 

Here's another way to compare fractions without having to worry about common denominators

 

Write  - (10 + 3/4)   as the improper fraction   -43/4

 

Now  let's compare these fractions

 

-43 / 4   ???   - 41 / 5

 

Multiply both sides by 5

 

(5) (-43)  / 4  ???  -41

 

Multiply both sides by 4

 

(5) (-43)   ???   (4) (-41)    

 

Simplify both sides

 

-215  ???  -164

 

Note that the left side is < the right side

 

This means that the original fraction on the left side (-43/4)   is smaller than the original fraction on the right side, (-41/5)

 

 

cool cool cool

 Sep 14, 2017

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