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Since it's Thanksgiving week, let's think about pie for a second. No, not mathematical pi, just actual real edible pies. For Thanksgiving I'm in charge of making dessert, so I'll be bringing two pies, one pumpkin and one apple. Let's say that I sliced the apple pie into 12 pieces, and the pumpkin pie, since it held together better, into 18. Fast forward to the end of the evening. My pies were a big hit, and I have almost none left. In fact, all I have is three pieces of apple and four pieces of pumpkin. I want to combine the remaining slices into a single pie pan, so that they take up less space in the fridge. How do I figure out if my remaining pie will fit in one pan? Well, let's start by writing down the remaining amounts of pie in the form of fractions. Remember, one of the definitions of a fraction is parts of a whole, so let's apply that definition to figure out our starting fractions. The apple pie was cut into 12 pieces, and we have three out... read more

Yes, there is only one way.  Let's say for example that we have a fraction of 2/3.  Now, the bottom number is the denominator which means the number of equal parts into which a whole circle most specifically is divided.  So the circle is divided into 3 equal parts.  On the other hand, the top number is the numerator which means how many equal parts out of all of them are lightly shaded inside the circle. So 2 out of all 3 equal parts of the circle are lightly shaded.   Now, the only way to change the number of equal parts without affecting the fraction value is to multiply it by any number you want which will also change the numerator.  So let's say for example that in the fraction of 2/3, if you wanted to divide each of those 3 equal parts into 2 further equal parts, you will have a new number of equal parts which is 6 (3*2=6).  This will affect the numerator 2 as well since this is included in the total number of equal parts, so each of the... read more

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