Question

Mark used a number line to model dividing 2 3 by 3. He divided the number line from 0 to 1 in 3 equal sections, and then divided each of those sections into 2 equal parts. Mark says 2 3 ÷ 3 is 1 3 . Is his answer correct? Explain why or why not.

Answer 1

No, his answer is not correct.

Explanation:

Given expression,

`(2)/(3)/ 3`

`=((2)/(3))/(3)`

`=(2)/(3* 3)`

`=(2)/(9)`

Thus, his answer is not correct.

By model :

Draw number line from 0 to 1 in 3 equal section,

Then divided each of those sections into 3 equal parts,

We get,

`(2)/(3)/ 3=(2)/(9)`

Answer 2

Mark's answer is incorrect because he divided the number line into 2 equal parts instead of dividing the number line into 3 equal parts.

Given the expression solved by mark using the number line expressed as:

`(2)/(3) / 3`

First, we need to simplify the given expression to be sure that the mark is correct as shown:

`=(2)/(3) / 3\\= (2)/(3) * (1)/(3)\\=((2* 1))/(3* 3)\\=(2)/(9)`

Hence Mark's answer is incorrect because he divided the number line into 2 equal parts instead of dividing the number line into 3 equal parts.