Question

Paula made this model to show the sum of two mixed numbers. Write the addition equation shown by the model and solve it.

You can write out the fraction names or use the forward slash (/) on your keyboard to represent the fraction bars.


A number line from zero to one partitioned into thirds. There is a gray rectangle above the number line stretching from zero to three and two thirds. To the right is a darker gray rectangle above the number line stretching from three and two thirds to six and one third.


Your answer:

Answer 1

`3(2)/(3) + 2(2)/(3) = 6(1)/(3)`

Explanation:

Given

See attachment for number line

Required

Determine the model

From the attachment, we can see that each partition is 1/3

The gray rectangle covers 11 partitions.

So:

`Gray = 11 * (1)/(3)`

`Gray = (11)/(3)`

Express as a mixed number

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

The black rectangle covers 8 partitions

So:

`Black= 8 * (1)/(3)`

`Black= (8)/(3)`

Express as a mixed number

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

So, the model is:

`Gray + Black = Total`

Where Total is the point where the black rectangle stops

`3(2)/(3) + 2(2)/(3) = 6(1)/(3)`