Question

insert five rational number Between –1/2and 2/3​

Answer 1

Answer:

There are a lot more than five of them. In fact there are infinitely many rational numbers between any two numbers (rational or irrational.

To illustrate, let’s find a method that will allow us to come up with 100 rational numbers in between 1/2 and 2/3.

• Step 1: make those two numbers comparable.

I won’t go on about common denominators, but that what we’re doing really.

1/2 = 3/6 and 2/3=4/6

So the difference between them is 1/6

• That difference is definitely less than, 1/10 (to make things easy for ourselves.

• So 1/2+1/1000, 1/2+2/1000, … 1/2+100/1000 are all rational numbers between 1/2 and 2/3

• Here’s one of them specified more completely

1/2+2/1000=500/1000+2/1000=502/1000

That isn’t expressed in its simplest terms (251/500) but is is certainly rational and certainly is between 1/2 and 2/3 as required.