I understand how to divide fractions by other fractions but want to know why this is a useful mathematical technique. When do you need/want to divide a fraction by another fraction? What’s it useful for? Is it a specialist thing or am I missing an obvious application?
In: Mathematics
Sometimes you get into a situation where you need to divide one number by another number and both those numbers happen to be fractions. It would be unfortunate if you didn’t know what to do when that happened, wouldn’t it? To give a more tangible example, let’s say I’m making a video game, and in this video game I have a spell that I want to deal more damage the lower the proportion of HP the enemy has, like a big finisher move. To do that, I might write its damage formula as:
Damage = (ATK * 2.5) / X, where ATK is the attack power of my character and X is the percentage HP the enemy has left – if it has 100% HP left, it’s 1, if it has 20% HP left, it’s one fifth (or in decimal form, 0.2). Now, since my character’s ATK value must be a whole number, 2.5x that number will often contain a fraction. If I have 17 ATK, then the number I’m dividing by X is going to be 42.5. Then to get my damage dealt, I can do 42 / 0.2 nice and easy, but then I’ll have to do 0.5 / 0.2. That’s a fraction divided by a fraction.
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