Question

On the following number line, two rational numbers are graphed. Represent the two numbers as fractions (or mixed numbers) in lowest terms, and write two different expressions to represent the difference between them. Then, find the difference, showing all of your work.

Answer 1

The lowest number is - 3/2 . The greatest number which is 5/6 .

Difference =
`(7)/(3)=2(1)/(3)`

Explanation:

The lowest number is - 3/2 . We can also write - 3/2 as
`-1(1)/(2)` . The greatest number which is 5/6 ( There are 6 equal spaces between each of the integers ).

We can write difference between these numbers as follows:

A.

`(5)/(6)-\left ( (-3)/(2) \right )\\\\=(5)/(6)+(3)/(2)\\\\=(5+9)/(6)\\\\=(14)/(6) \\\\=(7)/(3)\\\\=2(1)/(3)`

B.

Also, difference can be written as follows:

`(5)/(6) - (-1(1)/(2))\\\\= (5)/(6) + 1 + (1)/(2)\\\\= (5)/(6) + (6)/(6) + (3)/(6)\\\\=(5+6+3)/(6)\\=(14)/(6)\\\\=(7)/(3)\\\\=2(1)/(3)`

Answer 2

The lowest number is - 3/2 or -1 1/2 as a mixed number (answer)

The we have greatest number which is 5/6 (answer) ( note there are 6 equal spaces between each integer value).

Difference between these numbers can be written as 5/6 - (-3/2)

= 5/6 - (-9/6) = 5/6 + 9/6

= 14/6

= 2 1/3 Answer

Also, difference = 5/6 - (-1 1/2)

= 5/6 + 1 + 1/2

= 5/6 + 6/6 + 3/6

= 14/6

= 2 1/3 (answer)