Question

a. Divide: \(24 \div 8\) b. Do you get the same result by doing the division \(8 \div 24 ?\) c. Does the commutative property hold for division? That is, does $24 \div 8=8 \div 24 ?$

Short answer

Answer: No, the commutative property does not hold for division.

Step-by-step solution

Divide 24 by 8

To find the result of the division \(24 \div 8\), we need to calculate how many times 8 can fit into 24: \(24 \div 8 = 3\). The quotient is 3.

Divide 8 by 24

Now let's check if swapping the numbers gives the same result. We need to calculate how many times 24 can fit into 8, which is: \(8 \div 24\). As 24 is greater than 8, the quotient will not be a whole number. In this case, it is a fraction: \(8 \div 24 = \frac{1}{3}\).

Determine if the commutative property holds for division

Given that \(24 \div 8 = 3\) and \(8 \div 24 = \frac{1}{3}\), we notice that the results are different. Therefore, the commutative property does not hold for division, and we can conclude that \(24 \div 8\) does not equal \(8 \div 24\).