That’s right, Big Fat One. The idea here is to understand equivalency and how often the number one is used in mathematics. Consider the following:

1 = 1/1 = 5/5 = 2356/2356

Notice 1 can be written as a fraction and this fraction has many different "number names". If you understand the example above then you already understand equivalency which can apply to numbers other than one such as:

However, back to the number 1. We all know that 5 x 1 = 5 and 7/7 x 1 = 7/7 but when students look at the following:

they get confused. It is mostly because they have forgotten the ease of multiplying by 1 and that 3/3 or 9/9 (or millions of other number names) is the same thing. Sure, 8 x 3/3 is actually 24/3 first but then simplifies to 8/1 then 8 which is what we started with anyway. The idea is for you to recognize the use of one when working with numbers.

Common denominator, simplify, reduce. Have you heard any of the following math terms before? Well, they all revolve around the use of the number 1. But where’s the "big fat" part, you ask? Simple. Notice that 1 is pretty skinny as numbers go. If I exchange 1 for a number name like 17/17, for example, then we call it "big fat one" (BFO) to recognize that the numbers are wider YET we are still talking about the same old number: 1. This is way easier to show you than to explain in words:

1/3 + 1/4 = 1/3 x 4/4 (BFO) + 1/4 x 3/3 (BFO) = 4/12 + 3/12 = 7/12

You see? Adding 4/12 and 3/12 is really the exact same as 1/3 + 1/4 because we used BFO to find a common number name for both fractions. And since BFO is 1 we know that nothing has really been changed except the name. This is CRITICAL for you to understand as one of the foundational concepts in mathematics.

Now look at how it applies to simplifying 24/30:

24/30 ÷ 2/2 (BFO) = 12/15

12/15 ÷ 3/3 (BFO) = 4/5

Notice, it took two steps of using BFOs to get the fraction simplified. Is that O.K.? Of course! Don’t let anyone tell you different! Now, are there more efficient ways to do this? Again, of course. Think about it. If I had used 6/6 from the beginning, I could have simplified in just one step:

However, the only thing this does is save time which, I’ll admit, is important EVENTUALLY but, regardless, gets the same answer either way. FYI: using 6/6 instead of 2/2 then 3/3 is called using the greatest common factor (heard of it?) but this is a much better way to understand how it is found than other methods I’ve seen. Remember, the number of steps it takes to simplify is NOT IMPORTANT, what is important is that you do it correctly and completely.

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