Suppose she cut the cake into 8 equal size pieces and 6 people ate all the pieces. Explain how they could have divided the pieces so that everyone ate the same amount of cake. Show work in a drawing

your mum

I cut 6 identical cakes into 8 equal pieces each, and then 20 pieces were eaten. What would the mixed number be?????

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MATH

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To ensure that everyone eats the same amount of cake, you need to divide the 8 equal size pieces among the 6 people in a fair manner. Here's how you can do that:

1. Begin by drawing a diagram representing the 8 equal pieces of cake. You can draw a circle and divide it into 8 sections, like this:

_______
|__|__|__| (Each section represents one piece of cake)

2. Now, allocate the pieces to each person equally. Since 8 pieces need to be divided among 6 people, give each person one piece of cake initially.

Person 1: 🍰
Person 2: 🍰
Person 3: 🍰
Person 4: 🍰
Person 5: 🍰
Person 6: 🍰

3. After the first round, you will have 2 pieces left to distribute. To divide these remaining pieces equally, you have two options:

a. Cut both leftover pieces in half, resulting in four additional smaller pieces. Distribute one of these smaller pieces to each of the six people. Now each person has one full-sized piece of cake and one smaller piece.

_______
|__|__|__|__|__|__|__|__|
🍰 🍰 🍰 🍰 🍰 🍰

b. Alternatively, you can cut one of the leftover pieces into six equal parts. Distribute one of these parts to each person. Then, give the remaining whole leftover piece to any one person. Now everyone will have one full-sized piece, and one person will have an extra small piece.

_______
|__|__|__|__|__|__|__|__|
🍰 🍰 🍰 🍰 🍰 🍰
🍰

Both methods ensure that each person gets the same total amount of cake, but the distribution of smaller pieces varies slightly.

It's important to note that the drawings provided here are simplified representations. In reality, the pieces may not be perfectly even or neatly divided, but this approach demonstrates an equitable sharing of the 8 pieces among 6 people.

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8/6 = 1 2/6 = 1 1/3

Each person ate 1 1/3 pieces.