Thirty-two divided by 3

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Question from Shelly, a student:

Please look at page 63 question 16 from this link:

http://ritter.tea.state.tx.us/student.assessment/resources/guides/study/G7MathE-SG.pdf

The answer key says :
Question 16 (page 63)
A Correct. The triangle in the scale model and the
triangle formed by the ramp are similar figures.
The ratios of their corresponding sides are equal.
The height of the ramp (4 feet) corresponds to
3 inches in the model.
The length of the ramp (x feet) corresponds to
8 inches in the model.
Write a proportion by setting the ratios of the
corresponding sides equal to each other and then
solve the proportion.
4/3 = x/8

3x = 32 Use cross products.

x = 32/3 Divide both sides of the equation by 3.

x = 10 2/3 Divide 32 by 3: 32 / 3 = 10 R2.
The number 10 is the whole-number
part; 2 is the fractional part of
the mixed number.
The ramp will be 10 2/3
feet long.

What I don't get is why is it that 10 with a remainder of 2 ( 10 R2 ) equals 10 2/3? shouldn't it be 10 2/10 ????? please explain because I'm confused and I need to know this so I can pass my release test to go into public school for the first time ever. PLEASE ANSWER.

No, you are still dividing by 3.

Suppose you are trying to divide 32 bars of chocolate
among 3 people [Shelly, Tasha, and Unity]. Each person gets 10 and there are 2 left over. Visualize those two chocolate bars. Assume you've eaten one bar a day and now it's time to divide up the last two. You're hungry.

Now, Unity, who is sneaky, tries to tell you and Tasha that your share is 2/10 of a bar each (if there are ten squares in each bar, that is two squares for you and two for Tasha. Visualize those two squares. ) Unity will keep the rest.

Are you and Tasha going to let her get away with that? (No violence please!)

Good Hunting!
RD

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