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
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Convert your fractions to decimals and when you find your answer convert it back to a fraction. That’s why my dad drilled it into my head that its important to convert fractions to decimals and back
Lets look at integers to begin with….x * 4 == x + x + x + x; “x multiplied by four is the same as four of itself added together”
Similarly if we turn that multiplier down to 1 we see a problem like this….x * 1 == x + 0; “x multiplied by one is itself with nothing else added to it.”
Regarding fractions-
If we turn that multiplier down even more it becomes a fraction. Consider how we would add less than nothing or start out with less than the original number.
x * (2/3) == ((x*2)/3) + 0 == ***x + (- (x/3))***; “x multiplied by half is the same as x ***plus a third of itself less than nothing added to it***.
I’ve written the section in bold because I assume the regular “just multiply it by the numerator” solution wasn’t doing it for you. Instead, we’re adding like in the first to examples I gave but we are multiplying less than 1, and we are adding less than zero than x, we are adding a negative number.
[edit: incorrectly said “half”, as the equation is written we should add a negative third (subtract one third)]
This used to bug me a lot too, it clicked when I was thinking about areas. So, let’s say you multiply 2 lengths.
2m x 2m you get 4m2 (2 meters multiplied by 2 meters is 4 meters squared).
So, here the unit is changing from meters to meters squared (so, you are going from length to area). So, you are essentially making a big square with a side of 2m which is the same as 4 1mx1m squares = 4m2
Now, let’s think about fractions.
0.5mx0.5m is 0.25m2. Here, you are making a square with a 0.5m side, and if you think about a square with a side equal to 0.5 m, it would just take a quarter of space as a square with a 1m side which lines up perfectly.
So, we understand that the magnitude is going down, but forget that the units are changing in ways which increases the difference between them dramatically.
It’s a fraction of a fraction.
In the case of 1/2 “times” 3/5 it’s half of 3/5 which if you want to visualize it say you have a circle and say it have 5 places where you can out apples, place out three apples among those spaces. If the circle is one whole that’s 3/5 or 60%. Now that times 1/2 (which also is 0.5) mean you will just have half as many apples which you hopefully quickly figure out mean 1.5 apple. However with these things you aren’t supposed to answer 1.5/5 though that is the right amount. What you do instead is that you multiply the denominators so 2 * 5 resulting in 10 granting you spaces for 10 things and then the numerators 1 * 3 and you get three. So three out of ten spaces would be filled and you should answer 3/10 or 30% by visually you could see it as instead of having room for 5 whole apples you make room for 10 apple halves where you still place three halves but as you know three halves only make up 1.5 apple not 3. As in you divide all apples into 2 pieces and then keep as many pieces as you originally had.
Regardless of what we are talking of you can see the denominator as in how many pieces it’s split up and the numerator as how many of those pieces. So one full unit at first was split into 5 and you had 3 of those. But then you divide everything again in 2 and you have an equal amount of those meaning 3 of 10.
0.5 can’t find the sign 5 just mean half times half times half and so on which become smaller and smaller because you re cutting it in half the whole time.
For the apples cut them in half and keep as many pieces as before as said 3/10 if you visualize as apple halves. Maybe that just confuses things as 1.5 apple is more than 1 but now it was of potentially 5 and how full that circle was. Maybe this last part just fucked up. Depending on how you think the other way would be split the apple into five pieces. Now cut then apart again and you get 10 pieces. 1/2 x 3/5 is keeping 1 * 3 = 3 of those tenths of an apple. Denominator in the division being how many times you divide something into smaller parts and the numerator how many of those smaller parts you keep/have. In the case of multiplying these fractions you are dividing something already divided.
Isn’t the easiest way of explaining this just to say that it’s a means of expressing a fraction of a fraction?
The multiplication sign is simply an alternative way to write the word ‘of’.
(1/2) x (1/4) can be read as one-half of one-fourth. What is half of a quarter? An eighth.
(1/2) x (1/4) = (1/8)
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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Hi OP,
I know this has been explained, but I used to teach and write test prep manuals for one of THE BIG test prep companies, and I thought I might also provide a little insight on the most wonderful components of complicated math – percentages.
If I say to you “what’s 25% of 100”, it’s pretty easy to say “25”, right? We know 25% means a quarter, and one quarter of 100 is 25. It’s nice, it’s easy.
But WHY does 25% mean a quarter? What’s going on there?
Any time you see a percent sign, it means “divide by 100.” So if you take 25% and follow this rule, then 25% means 25/100. And you can reduce that down to 1/4. [Fun fact, quarter comes from the latin *quattor*, meaning four. You need four quarters to make the whole of something. That’s why, in fluid FREEDOM measurements, there’s four quarts to a gallon).
(so, other users have talked about OF meaning multiply): 25% of 100 can be thought of as 25/100 *aka 25 percent* times *aka of* 100.
25/100 is 1/4. 1/4 multiplied by 100 is 25.
I hope this makes sense so far. So when you hear that a credit card might be offering an 8% interest rate, the way to think about that is:
8/100 (because remember, percent means divide by a hundred) times the amount you’ve borrowed.
Now, the cool thing is that this is a kinda interesting way to get into multiplying fractions! If you have 50% of a banana, you have (50/100) of a banana. That reduces to 1/2, and that means you have a half of that banana.
But then what happens if you’re gonna make a sandwich and you need 25% of the remaining banana? You take that 25% (25/100 aka 1/4) and multiply it by what you still have (1/2 banana).
(1/2) (aka the amount of banana you currently have) * 1/4 (the amount you need for your delicious sandwich), which gives you 1/8. Your sandwich will need 1/8 of one whole banana.
One additional fun fact is that percent literally comes from per (meaning for) and cent (meaning one hundred). If I told you I had 5 laptops for every one hundred students, that would mean 5 *percent* of students get laptops. That’s why you can think about percent meaning divide by a hundred.
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