Anothony bought an 8ft board. He cut off 3/4 of the board to build a shelf and gave 1/3 of the rest to his brother for an art project. How many inches long was the piece Anthony gave to his brother?

Let's break the problem down step by step:

1. **Total length of the board**: Anthony's board is 8 feet. To work in inches, convert feet to inches:
   \[
   8 \, \text{feet} = 8 \times 12 = 96 \, \text{inches}.
   \]

2. **Length of the board used to build the shelf**: Anthony cut off \( \frac{3}{4} \) of the board for the shelf. This means he used:
   \[
   \frac{3}{4} \times 96 = 72 \, \text{inches}.
   \]

3. **Remaining length of the board**: After cutting off the shelf, the remaining length is:
   \[
   96 - 72 = 24 \, \text{inches}.
   \]

4. **Length given to his brother**: Anthony gave \( \frac{1}{3} \) of the remaining 24 inches to his brother. So, the piece given to his brother is:
   \[
   \frac{1}{3} \times 24 = 8 \, \text{inches}.
   \]

Thus, the piece Anthony gave to his brother was **8 inches long**.

Would you like any further details or explanations?

Here are 5 related questions to expand on the concept:
1. How much of the board did Anthony keep for himself after giving a piece to his brother?
2. What fraction of the total board did Anthony give to his brother?
3. If the board had been 10 feet long, how much would Anthony have given to his brother?
4. How long would the remaining piece have been if Anthony hadn't given any to his brother?
5. What percentage of the original board was used to build the shelf?

**Tip**: When solving word problems, converting units (like feet to inches) early on can simplify calculations and prevent mistakes later.

Anthony bought an 8ft board. He cut off 3/4 of the board to build a shelf and gave 1/3 of the rest to his brother for an art project. How many inches long was the piece Anthony gave to his brother?

Learn how to solve a fraction-based word problem involving cutting an 8ft board. This step-by-step solution shows how to convert units, calculate fractions of a length, and determine the length given to a brother. Suitable for Grades 5-7 students learning about fractions and unit conversions.

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