Sometimes applying properties of operations makes multiplying rational numbers easier and quicker.
Let's take a look at Arnold's posts:
I am going to post an example of associative property of multiplication to solve 2 over 3 times open parentheses 3 times 4 over 7 close parentheses. Applying the associative property to change the grouping gives me open parentheses 2 over 3 times 3 close parentheses 4 over 7, which makes it easier to multiply since the 3's would cancel each other out.
Post an example of where using properties of operations makes multiplying rational numbers easier and quicker.
Reply to two of your classmates' post evaluating the usefulness of the property of operations they used.
Example: Let's say we want to solve 4/5 times (2/3 times 3/4). By applying the associative property of multiplication, we can rearrange the grouping as (4/5 times 2/3) times 3/4. This allows us to multiply the numerators and denominators separately, resulting in (4 times 2) over (5 times 3) times 3/4. This simplifies to 8/15 times 3/4. Now, we can multiply the numerators and denominators again, giving us (8 times 3) over (15 times 4), which simplifies to 24/60 or 2/5.
By using the associative property of multiplication, we were able to simplify the problem and make calculations quicker. Instead of multiplying all three fractions at once, we broke it down into simpler steps, which is a useful strategy when dealing with complex rational numbers.