#### Why doesn't the inequality symbol change when multiplying or dividing positives?

Anonymous

1

Mahesh Godavarti

0

Great question. This is also related to the question on why the inequality symbol flips when multiplying or dividing by a negative number.

Please take a look at the following discussion.

Sangeetha Pulapaka

0

Hmm,,, let us see if I can answer this.
I have two numbers 6 and 2 We know that 6> 2 on the number line
Let us first multiply it with a positive number on either side
When I multiply +6 on both sides, I get 6(+6) > 2(+6)
36 > 12 which is also true So, there is no need to flip the inequality in the middle.
When I multiply with -6 on both sides without flipping the inequality in the middle,
I get 6(-6) > 2(-6) or -36 > -12. Is this true? No, -36 \ngtr -12
because as we move down the number line, as the negative number increases its value decreases.
So this means that when I multiply with a negative number, the inequality will have to change
So we make it a point to flip the inequality when we multiply this with a negative number
Look at 6> 2 again
This time I multiply with -6 on either side, and I also flip the inequality
6(-6)< 2(-6)
-36 < -12
This is true.