Finding Rational Numbers Between Other Rational Numbers.

[sleepnix]

Hello. I need help with all steps of finding rational and irrational numbers between rational numbers. For example, "What rational number lies two-fifths of the way between -3/5 and 1/2." Is there a formula, or something basic I can do that will work for ALL of these kinds of questions? At the very least, please solve my example. Your help is greatly appreciated!

 

[Deleted member 4993]

Hello. I need help with all steps of finding rational and irrational numbers between rational numbers. For example, "What rational number lies two-fifths of the way between -3/5 and 1/2." Is there a formula, or something basic I can do that will work for ALL of these kinds of questions? At the very least, please solve my example. Your help is greatly appreciated!

Do you know how to show rational numbers (approximately) on a number line?

If you do, then show those numbers - on the number line - and choose any number lying between those.

For example - I want to find a number between 2 and 5.

so i draw my number line and plot the given numbers on that:



....(-2).........(-1).........(0).........(1).........(2).........(3).........(4).........(5).........(6).....

....................................................... (2) ..................................(5).................

So numbers between those could be 2.5, 3.7 , 4.2 ... whole lot of numbers.....

I missed the part of ratio in my first response.

Suppose I want to find a number 2/5 th distance (between 2 and 5) away from 2 towards 5 (your problem does not tell this part - making it somewhat ambiguous)

distance between 2 and 5 = 5 -2 = 3

2/5 th of that (3) = 3 * 2/5 = 1.2

so 1.2 away from 2 (towards 5 meaning increasing) = 2 + 1.2 = 3.2

 

[Loren]

Let a represent the smaller of the two numbers.
Let b represent the larger of the two numbers.
Let r represent the ratio.
Let x represent the sought after number.

x = r(b-a)+a

In your example: What rational number lies two-fifths of the way between -3/5 and 1/2.

a = -3/5
b = 1/2
r = 2/5

x = (2/5)(1/2 + 3/5) + (-3/5) = -4/25