After a course potluck, Emily has three equally sized apple pies left and she desires to division them right into eight equal portions to provide to eight students who desire to take some pie home.

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Draw a snapshot showing exactly how Emily can divide the pies into eight equalportions. Describe how your snapshot shows eight equal portions.What fraction of a pie will certainly each that the eight students get?Explain how the answer come (b) is related thedivision problem $3 \div 8$.

## IM Commentary

The function of this job is to aid students view the connection in between $a \div b$ and $\fracab$ in a certain concrete example. The relationship in between the department problem $3 \div 8$ and also the portion $\frac38$ is actually an extremely subtle.

$3 \div 8$ is the number you main point 8 through to obtain 3.

$\frac38$ is the number you gain by acquisition 3 copies of the unit fraction $\frac18$.

So $3 \div 8$ is defined in terms of multiplication, and also $\frac38$ is characterized in terms of unit fractions. The is not obvious that these 2 numbers are the same, therefore students need avenues to watch that they will certainly necessarily constantly be the same. Keep in mind that if $b$ human being share $a$ pies equally, climate each person will get $\fracab$ of a pie by the exact same kind of reasoning shown in the systems below.

This task is probably ideal suited for instruction or developmental assessment.

## Solution

Below is a snapshot of how Emily can divide the 3 apple pies right into eight equal portions. Below each shade (yellow, orange, red, green, blue, dark purple, irradiate purple, and light blue) to represent one portion. For this reason each section consists of three pieces of pie and each item of pie to represent $\frac18$ the a complete pie:

Because these pies space all the exact same size and they space all apple pies, Emilydoes not require to give each college student one item of each of the three pies: 2 or 3 pieces that the same pie can go come one student. Thispicture, however, shows clearly that the pies have been divided into eight same portions. If multiple piece of a specific pie were to go to the very same student, it would certainly be vital to analyze the picture an ext closely and also count how plenty of slices the pie each student received to examine that it has been separated evenly.

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As the photo shows, each portion consists of three slices of apple pie. Since these slices stand for $\frac18$ that a pie, this method that each student gets$\frac38$ of an apple pie.

If 3 pies are separated into 8 same portions, climate 8 that these portions makes 3 pies, a fact that is plainly illustrated in component (a). We can write this in icons if we usage a question note to represent the amount of pie in one portion:$$8 \times ? = 3$$When we recognize a factor and the product, us can discover the other factor by dividing:$$3 \div 8 = ?$$So one person"s portion is whatever we get when we divide 3 by 8.In component (b), we saw that one section is $\frac38$. So that means that$$3 \div 8 = \frac38.$$