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In Mathematics / College | 2025-07-07

A board that measures [tex]\frac{3}{4}[/tex] feet long is cut into 6 pieces. What is the length of each piece?

A. [tex]1 \frac{1}{2}[/tex] inches
B. 3 inches

Asked by taylor4shays

Answer (1)

Convert the length of the board from feet to inches: 4 3 ​ feet = 9 inches .
Divide the total length by the number of pieces: 6 9 ​ = 2 3 ​ inches .
Simplify the fraction: 2 3 ​ = 1 2 1 ​ inches .
The length of each piece is 1 2 1 ​ inches ​ .

Explanation

Understanding the Problem We are given a board that is 4 3 ​ feet long and is cut into 6 pieces. We need to find the length of each piece in inches and choose the correct answer from the given options.

Converting Feet to Inches First, we need to convert the length of the board from feet to inches. Since 1 foot = 12 inches, we have 4 3 ​ feet = 4 3 ​ × 12 inches.

Calculating Total Length in Inches Calculating the length in inches: 4 3 ​ × 12 = 4 3 × 12 ​ = 4 36 ​ = 9 inches. So, the board is 9 inches long.

Dividing to Find Length of Each Piece Now, we need to divide the total length of the board (9 inches) by the number of pieces (6) to find the length of each piece: 6 9 ​ inches.

Simplifying the Fraction Simplifying the fraction: 6 9 ​ = 3 × 2 3 × 3 ​ = 2 3 ​ inches. Converting this to a mixed number, we get 1 2 1 ​ inches.

Final Answer Comparing our result with the given options, we see that the length of each piece is 1 2 1 ​ inches, which corresponds to option A.


Examples
Imagine you are a carpenter and you have a wooden plank that is 4 3 ​ feet long. You need to cut it into 6 equal pieces to build a small decorative item. Knowing how to divide the total length into equal parts helps you determine the exact length of each piece, ensuring that your final product is symmetrical and aesthetically pleasing. This skill is essential in woodworking and many other crafts where precision is key.

Answered by GinnyAnswer | 2025-07-07

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