Question

Find ten rational numbers between 3 by 5 and 4 by 5 ​

Answer 1

$\frac{3}{5} \times \frac{11}{11} \\ = \frac{33}{55}$

$also \: \frac{4}{5} \times \frac{11}{11} \\ \\ thus \: 10 \: rational \: numbers \: are \: -$

$\frac{34}{55} \\ \\ \frac{35}{55} \\ \\ \frac{36}{55} \\ \\ \\ \frac{37}{55} \\ \\ \frac{38}{55} \\ \\ \frac{39}{55} \\ \\ \frac{40}{55} \\ \\ \frac{41}{55} \\ \\ \frac{42}{55} \\ \\ \frac{43}{55}$

Answer 2

Answer:

Step-by-step explanation:

Rational numbers are numbers that can be expressed in a ratio for example

1.5 = 3/2 .. 1.5 is half of 3 !

so all you have to do is find numbers like 3.1 , 3.25 etc

now... how do we 'rationalize'(turn percentage into ratios) them?

stay with me on this one

if we are adding a percentage like 0.5 for example

What does it mean? It is half of 1 !

0.25 is 1/4 of 1!

If you are crossing a road of length 1km and you cross 0.25km then you have crossed one fourth of the road!

Now heres how you find the ratio

Lets take 0.25 for this one !

multiply it with 100 ( 0.25 x 100 ) = 25

Now show it in a ratio with 100 like this

25/100 ( 25 out of 100 is same as saying 0.25 out of 1 )

now make the smallest number you can

We can start of by dividing both sides by 5

that gives 5/20

now lets divide both sides by 5 again

we get 1/4!

thats it so you can write 3.25 like 3¹/₄

If you want to rationalize this more you can multiple 3 with the denominator and add the numerator with it

3¹/₄ will be ((3x4)+1)/ 4 or 13/4

Lets do one more example

3³/₂

this will be ((3 x 2)+1)/2 or 7/2

find the other numbers between 3 and 5 like this