Question

$30$-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. Both statement A and statement B are correct.
• B. Statement A is incorrect and statement B is correct.
• C. Statement A is correct and statement B is incorrect.
• D. Both statement A and statement B are incorrect.

Answer 1

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

$WoodenboardA:$


$30$-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 $equalto\frac{15}{4}ft.$
Thus, the length of each piece is $greaterthan\frac{13}{4}ft.$

$WoodenboardB:$

$48$-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
The length of one piece of wooden board A is greater than $\frac{13}{4}ft.$
So, both Statements A and B are correct.