I am reteaching myself math, but something is bugging me soooo bad and I can’t find the answer. What is a real life example of multiplying a fraction by a fraction? I was wondering why .05 to the 5th exponent would get smaller not bigger. This is driving me bonkers.
Sure 1/2 makes sense, but how about 1/2 times 3/5 in real life?!?
Edit: OMFG. Math is cool and makes sense. Finally, I’m 28. Thank you all!!!!
Edit: I was given an AP Scholar award, but it was not for math.
* * * The best explanation goes to the person who explained “times” and “of” were synonomous!!!! * * *
NOW EXPLAIN THIS: How am I in the 99.9th percentile for arithmetic, but suck at math?! Do I have potential? Am I still gifted in “math” or are math and arithmetic too separate things. A professor told me they are different parts of the brain.
In: Mathematics
If I start with a whole pie and cut it in half I’d get 1/2 of a pie.
Now read this and every time I say cut think multiply.
If I start with a whole pie (1) and cut (multiply) it in half (1/2) I’d get 1/2 of a pie. 1 x 1/2 = 1/2
Now let’s try this with 1/2 x 1/2.
If start with a half of a pie and cut it in half I’d get 1/4 of a pie.
If I start with a half of a pie (1/2) and cut (multiply) it in half (1/2) I’d get 1/4 of a pie.
Multiplying Fractions are hard to visualize because you’d think multiplying makes it bigger.
I thought about the same question a few weeks ago.
There are two ways to think about division. One works for some cases but the second way works for all (including fractions).
1. a / b = c, means that divide a into b parts and each part is c. It works for most cases but not for others, like doesn’t make sense for fractions divided by fractions because you can’t break something up in fractional parts
2. a / b = c, means that you need c number of b’s to make up a
Like 1 div 2 = 1/2 means you need half of 2 to make 1.
And 1/2 div 1/4 = 2 means you need 2 quarters to make a half which also makes sense.
You have one (1/1 or 1.0) pie. I cut it in half (0.5 or 1/2) and take that piece away.
You now have 1/2 of a pie. I cut that piece in half (0.5) and take that piece away.
You now have 1/4 of the pie. 0.5 * 0.5 = 0.25. 1/2 * 1/2 = 1/4.
Another way to think of it is multiplying fractions is the same as dividing. 1/2 is another way of expressing 1 divided by 2
A REAL life example:
You’ve been feeding your dog 2/3 cup of brand A kibbles each meal according to the instructions. Then here comes brand B kibbles, a higher quality food for your dog and you’re supposed to give 2/3 cup each meal as well.
Since you don’t want to shock your dog’s digestive system (and result in horrific diarrhoea), you ought to gradually decrease the proportion of brand A kibbles and increase the proportion of brand B kibbles over the course of 5 days or longer.
So here’s the meal plan gonna look–
Day 1: (2/3)X(4/5) cup of brand A + (2/3)X(1/5) cup of brand B
Day 2: (2/3)X(3/5) cup of brand A + (2/3)X(2/5) cup of brand B
Day 3: (2/3)X(2/5) cup of brand A + (2/3)X(3/5) cup of brand B
Day 4: (2/3)X(1/5) cup of brand A + (2/3)X(4/5) cup of brand B
Day 5: (2/3)X(0/5) cup of brand A + (2/3)X(5/5) cup of brand B
Yup, this is a real life example… None of those cutting up pizza/pie crap. Who doesn’t eat the entire thing in one sitting?
I have not seen this being addressed, but my comment here would be that you are trying to continuously anchor mathematics in intuition. That eventually only gets you so far. From a certain point on in mathematics you inevitably leave the grounds of the innately familiar, and move to using the power of applying rules that will give you the right answer, WITHOUT being intuitive. I would argue that separation from intuition is what makes mathematics so powerful.
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I’m surprised I didn’t see any visual representations of multiplication here. Check out this website to see what multiplication of fractions looks like.
https://www.origoeducation.com/blog/focus-on-fractions-a-visual-model-to-teach-multiplication-and-division-of-fractions/
It makes a little more sense if you think about what multiplying is doing in general: it’s sorting things into groups.
When you multiply 2 X 4 what you’re saying is “I want 2 groups of 4.”
So with your example of (1/2) X (3/5) you’re saying “I want half a group of 3/5.” And that’s why the answer (3/10) is smaller and than the original 3/5.
And bonus round: when you divide what you’re asking is “how many groups of one thing does it take to make another?”
So example, if you’re dividing 4 by 2, you’re asking how many groups of 2 are there in 4.
So if we’re dividing (1/2) by (1/4), we’re asking “how many groups of 1/4 does it take to make 1/2?” And this is why the answer is 2.
This is why fractions get smaller when you multiply and larger when you divide.
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The answer you’re looking for is something you haven’t really thought to ask: what does the operation “times” mean in everyday English?
Say “of” whenever you see the times symbol.
Hope that clears up your confusion 😉
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