Give an example of a problem involving multiplication of fractions that can be made easier using the commutative property. Explain how it makes the problem easier.
One example of a problem involving multiplication of fractions that can be made easier using the commutative property is as follows:
Problem: Multiply 2/3 by 5/6.
To solve this problem, we can use the commutative property, which states that the order of multiplication does not affect the result. This means that we can multiply the fractions in any order and still get the same answer.
Step 1: We can start by multiplying the numerators together: 2 * 5 = 10.
Step 2: Next, we multiply the denominators together: 3 * 6 = 18.
Step 3: Now, we can simplify the fraction if possible. In this case, 10/18 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. This yields 5/9.
Using the commutative property, we can also multiply the fractions in the opposite order to get the same answer:
Step 1: Multiply the numerators together: 5 * 2 = 10.
Step 2: Multiply the denominators together: 6 * 3 = 18.
Step 3: Simplify the fraction: 10/18 = 5/9.
By using the commutative property, we have the flexibility to choose the order of multiplication, which can sometimes make the calculations easier or more convenient. In this example, multiplying the fractions in the opposite order does not change the result. Therefore, we can choose the order that allows us to work with smaller numbers or simpler calculations, making the problem easier to solve.