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CCSS.Math:

we're asked to multiply 5/6 times 2/3 and then simplify our answer so let's just multiply these two numbers so we have 5 over 6 times 2 over 3 now when you're multiplying fractions it's actually a pretty straightforward process you just multiply the new numerator the numerator of the product is just the product of the two numerators or your new top number is the product of the other two top numbers so our new the numerator and our product is just 5 times 2 so it's equal to 5 times 2 over 6 times 3 over 6 times 3 which is equal to 5 times 2 is 10 and 6 times 3 is 18 so it's equal to 10 18s and you could view this as either two thirds of five sixths or 5/6 of two thirds depending on how you want to think about it and this is a right answer it is 10 18s but when you look at these two numbers you immediately or you might immediately see that they share some common factors they're both divisible by two so if we want it in the lowest terms we want to divide them both by two so divide 10 by 2 divide 18 by 2 and you get 10 divided by 2 is 5 18 divided by 2 is 9 now you could have essentially done this step earlier on you could have done it actually before we did the multiplication you could done it over here you could have said well I have a 2 in the numerator and I have something divisible by 2 in the denominator so let me divide the numerator by 2 and this becomes a 1 let me divide the denominator by 2 and this becomes a 3 and then you have 5 times 1 is 5 and 3 times 3 is 9 so it's really the same thing we did right here we just did it before we actually took the product you could actually do it right here so if you did it right over here you'd say well look these are eventually going to 6 times 3 is eventually going to be the denominator 5 times 2 is that eventually going to be the NAM the numerator so let's divide the numerator by 2 so this will become a 1 let's divide the denominator by 2 this is divisible by 2 so that'll become a 3 and it'll become 5 times 1 is 5 and 3 times 3 is 9 so either way you do it'll work if you do it this way it kind of you get to see the fact things factored out a little bit more so it's usually easier to recognize what's divisible by what or you could do it at the end and put things in lowest terms