Question

Two​ 8-foot-long 2​ × 4s are cut into sections of equal length. Board A is cut into 9 equal​ sections, of which 5 are used. ​ Therefore, of the board has been​ used; of it remains. Board B is cut into 7 equal​ sections, of which 4 are used. That means of the board has been​ used; of it remains. Which has the longest remaining​ section, Board A or Board​ B?

Answer 1

Answer:

Board A

Step-by-step explanation:

Since the boards were split into equal sections, we can think of them as fractions.

$\frac{5}{9}$ of Board A was used, meaning $\frac{4}{9}$ of Board A remains.

$\frac{4}{7}$ of Board B was used, meaning $\frac{3}{7}$ of Board B remains.

To give these fractions common denominators, we multiply the numerator and denominator by the opposite denominator.

4/9 * 7/7 = 28/63

3/7 * 9/9 = 27/63

28/63 is greater than 27/63. This means that Board A has the longest remaining section.