Question

$A30$ -feet-long wooden board A is cut into $8$ equal pieces. $48$ -feet-long wooden board B is cut into $16$ equal pieces. Which of the following statements is true?
Statement 1: Length of one piece of wooden board $A<$ length of one piece of wooden board B
Statement 2: The length of one piece of wooden board A is greater than $\frac{13}{4}$ feet.

• A. Statement A is correct and statement B is incorrect.
• B. Statement A is incorrect and statement B is correct
• C. Both statement A and statement B are correct.
  
• D. Both statement A and statement B are incorrect.

Answer 1

The correct option is C Both statement A and statement B are correct.


Wooden board A:

$30$ -ft-long wooden board A is cut into $8$ equal pieces.
So, division statement $=30÷8$
Fraction of each piece $=\frac{30}{8}$
$=\frac{30÷2}{8÷2}=\frac{15}{4}$

Thus, the length of each piece is equal to $\frac{15}{4}$ ft.
Thus, the length of each piece is greater than $\frac{13}{4}$ ft.

Wooden board B:

$48$ -ft-long wooden board B is cut into $16$ equal pieces.
Length of each piece of board $B=\frac{48}{16}=4ft=\frac{16}{4}ft$
Therefore,
Length of one piece of wooden board $A<$ length of one piece of wooden board B