SOLUTION: I am learning division of fractions. I have an application problem that I do not understand. Here it is: A 5/8 karat diamond was purchased for $1200. What would a similar diamond w

Question 535649: I am learning division of fractions. I have an application problem that I do not understand. Here it is: A 5/8 karat diamond was purchased for $1200. What would a similar diamond weighing 1 karat cost?
thank you so much,
Kristie
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If a 2 karat diamond costed $5600, you would have no problem calculating that the price per karat (in $) is

You would just divide price by karat weight.
In your case, the calculation would involve dividing the price by 5/8 to find the price per karat.

In general, to divide by a fraction, you simply multiply by the upside down fraction. To divide by 5/8, you multiply by 8/5. It works the same way with any numbers.
The reason that division by fractions works that way can be shown with an example. Suppose you have 4 pizzas and you know that each of your brothers will quickly wolf down 5/8 of a pizza. How many brothers can you feed? To find how many times you can get 5/8 out of 4, you would first find how many times you have 1/8 there. To do that you multiply by 8 to get 4X8=32. That's how many eights (1/8 of a pizza slices) there are in 4 (pizzas). So you have 32 slices. To find how many packets of five of those slices (eights) you can make, you then divide 32 (4X8) by 5. So you multiply by the denominator of the fraction, and then divide by the numerator. It is the same as multiplying by the upside-down fraction. We call it the reciprocal fraction). In the end you would get 4X8/5=32/5=6.4 (or 6 and 2/5) portions of the size those brothers eat. If you have 7 or more brothers, someone will be left hungry. If you have 6 or less brothers, you get to eat too. I guess I was lucky that I had only one brother, although my sister ate a lot too.
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