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
Think of multiplication as adding up several sets of something.
For example, say you have 3 sets of 4 apples.
If you draw out this array and count up all the apples, you have a total of 12. This represents 3 x 4 = 12.
All multiplication can be expressed this way.
Now imagine you have 1/2 a set of 4 apples. If you draw out the set of 4 apples and take half of it, you have 2 apples. This represents 1/2 x 4 = 2.
Hope this helps!
Replace the word “times” with “of”
1/2 of 3/5. Half of 3/5. Obviously it’s going to be smaller than 3/5
0.05 of 0.05, that’s 5 percent of 0.05. You know 5 percent is a relatively small chunk of the original.
The problem may be you were taught only the abstract math rules, but it wasn’t well tied into concrete example that would build the numerical understanding.
I’m late to the party, but I’ll give another real-world example of multiplying fractions. This is more related to how ratios and fractions are the same thing.
Let’s say that 3/5 of everyone is resgistered to vote, and 1/2 of the registered voters will vote on election day. I want to know what fraction of everyone will vote on election day.
The answer is (3 registered voters / 5 total people) * (1 voter on election day / 2 registered voters) = 3 voters on election day / 10 total people (or 30% of everyone). The “registered voters” units cancel out from the top of the 3/5ths and the bottom of the 1/2.
Edit: I’ll agree that 3/5ths is a…not great number to use in the context of voting, but it was the example OP wanted. I could’ve gone with a different analogy, but voting is topical, haha.
Think of “times” as “of.” 3 X 5 = 3 of 5. 4 times 8 is 4 of 8, which is 32.
Same with fractions “one-half times one third” is “one-half of one-third.” Draw a picture. The answer is “one-sixth.” It does indeed make sense.
Think of division as “how many ____ go in ____?” 3 divided by one-half is asking “How many one-halfs can fit in 3?” the answer is 6. Draw a picture. It makes sense.
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Just replace the multiplication sign with ‘of’.
1/2*1/2=1/2 of 1/2.
3/10*2/5=3/10 of 2/5.
It is that easy. 1/2 of 3/5. You have 3/5 of a pizza to start with and the answer is 1/2 of that amount of pizza.
Always start with a simple problem to remind yourself of the pattern. 1/2 of something, maybe.
1/2 of 3/32 is 3/64, but write it so the numbers are above and below the diving line, not side by side.
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Another approach is to draw a rectangle and divide it in 1/2 vertically. Next, on the same rectangle but horizontally, divide the rectangle into 5. There will be 10 small rectangles. Next Colour in 1/2 vertically and 3/5 horizontally. Where squares are coloured twice that’s the multiple.
Can also do similar for addition, subtraction and division. Particularly with mixed fractions, this approach is far than the process usually taught in schools.
I teach elementary school (2nd grade) math, and I like to teach my kids to replace “times” with “groups of” – like “2×2” would be “2 groups of 2” and “.5x.5” would be “.5/half of a group of .5” or .25 – I don’t really teach division so I haven’t had to come up with a clever oversimplification, but I hope at least that one helps!
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