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# math

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

Sep 14, 2017

#1
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-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
+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)   Sep 14, 2017