Explain why 3.15>3.14

[Aion]

Hey. I know this seem trivial... But how would you prove this given that the definition of a fraction is a point on the number line, and a whole number m is smaller than another whole number n if m is to the left of n. And suppose we expand on this fact and define a fraction A to be smaller than another fraction B, if A is to the left of B on the number line.

Also how do you prove that two fractions are equal i.e. the same point?

 

[Aion]

I thought I needed to use move different segments on the number line for a specific sequence of nths to compare their lengths. But obviously 315 >314. So 315/100 > 314/100. lol

 

[Steven G]

If A-B>0, then A>B.
Proof: Suppose A-B>0. Now add b to both sides. Then A>B

Also: if A-B=0, then A=B
Proof: Suppose A-B=0. Now add B to both sides. Then A=B

 

[Steven G]

I thought I needed to use move different segments on the number line for a specific sequence of nths to compare their lengths. But obviously 315 >314. So 315/100 > 314/100. lol

If A>B, then C*A>C*B if C>0. If A>B, then C*A<C*B if C<0.
Also note that all division problems can be converted to multiplication problems (and visa versa!)

 

[Aion]

Yeah but I've haven't gotten to subtraction of fractions yet let alone multiplication. Thanks anyway! Also it's nice to be back, I've been kinda lazy with math, but I intend to do more math now and get into college. You guys are really doing some hard work by the look of things ;o
I'll try to contribute when I ask for a question in someway ... but I'm now sure how, since you answer every question so quickly