A board is 20 6/7  in. long. If it must be divided into three pieces of equal​ length, how long must each piece​ be?

The length of the board is \( 20 \frac{6}{7} \) inches. To divide it into three equal pieces, we need to divide the total length by 3.

First, convert the mixed number \( 20 \frac{6}{7} \) to an improper fraction:

\[
20 \frac{6}{7} = \frac{20 \times 7 + 6}{7} = \frac{140 + 6}{7} = \frac{146}{7}
\]

Now, divide the improper fraction by 3:

\[
\frac{146}{7} \div 3 = \frac{146}{7} \times \frac{1}{3} = \frac{146}{21}
\]

To simplify the fraction \( \frac{146}{21} \), check if it can be reduced. Since 146 and 21 have no common factors, it is already in its simplest form.

So, each piece will be \( \frac{146}{21} \) inches long, which can also be written as a mixed number:

\[
\frac{146}{21} = 6 \frac{20}{21}
\]

Thus, each piece must be \( 6 \frac{20}{21} \) inches long.

Would you like further details or have any questions?

Here are five related questions to further explore the topic:
1. How would you divide a board of different length into equal parts?
2. How can you convert any mixed number to an improper fraction?
3. What is the process for simplifying fractions?
4. Can you calculate the length of each piece if the board were 30 5/8 inches long?
5. What if the board was to be divided into 4 equal parts instead?

**Tip:** When dividing mixed numbers, always convert them to improper fractions first for easier calculations.

A board is 20 6/7 in. long. If it must be divided into three pieces of equal​ length, how long must each piece​ be?

Learn how to divide a 20 6/7 inch board into three equal parts. This problem involves key mathematical concepts like converting mixed numbers to improper fractions and dividing fractions. The detailed solution is perfect for students in Grades 6-8.

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