Question

a. A friend is having trouble comparing rational numbers. Write an explanation that will tell your friend how to decide if a rational number is greater than, less than, or equal to another rational number. Consider positive and negative numbers in your answer.

Answer 1

First, we need to know the rational numbers are numbers in this way

`(a)/(b)`

where a is the numerator and b the denominator

But first, we need to know another thing first the negative and positive numbers

if the number is greater but have a negative number this means this number will be less than the other

for example

-5 is less than -2

-4 is less than 0

-1 is greater than -5

Now if we talk about rational numbers is like we dived a cake if we dived the cake in two parts is more cake if we dived the cake in 5 parts

one half is greater than one fifth

`(1)/(2)\text{ > }(1)/(5)`

Here some other examples

`(10)/(4)>(15)/(6)`

Is this true? Why?

You can always do the division in order to compare your answer

the truth is the numbers are equals, always help if you can simplify the fraction to the smallest one

`(10)/(4)=(5)/(2)`
`(15)/(6)=(5)/(2)`

One tip is always simplify

You can know who is bigger base normally in the denominator is the denominator of one fraction is greater than the other denominator normally the greater fraction will be the one with the smallest denominator.

To confirm is always a good idea to do the division

5/2=2.5

this helps to clarify