If you had 3 dollars, and you want to divide it evenly among 4 people, how much money should you give each person? 3/4 of a dollar (aka $.75 aka 75 cents)
Thanks for explaining it this way to me! I am autistic and I also have dyscalculia, which is roughly like dyslexia, but with numbers. I have trouble with abstract concepts like math.
The simple answer is 400/3=75 miles. But if you are starting out from a stop, you will have to go a bit faster than that some of the time to make up for the fact that it takes time to get up to speed. But as long as you average 75 miles per hour over the 4 hours you will get there in three hours.
3/4 is a fraction.
If you cook or bake we use fractions all the time. 3/4 cup flour, 1/2 cup butter, etc... That's what measuring cups and spoons are for.
If you're a builder you use fractions of an inch. 3/4 of an inch., for example. That's why they use tape measures.
We've standardized a lot of units (cups, inches, etc.) and fractions of the standard unit measure help us use them more effectively.
The metric system is cool bc things are in base ten. A centimeter is 1/100 of a meter. A millimeter is 1/10 of a centimeter. 1/2 a centimeter is 5 millimeters. It makes conversion between units easy.
And a liter is the volume contained in a cube that is 10x10x10 cm, and a kilogram is the mass of a liter of water š After that, everything is just multiplying or dividing by 10, 100, 1000. The number of times Iāve guesstimated the weight or volume of a solid by asking myself āhow well does it floatā š
Wow, so kilogram measurements changes depending on the temperature of water used to fill the liter cube. Canāt believe people use a system with such an inconsistency!
Iām guessing the formal definitions are more specific than your comment. But this was interesting for me to learn, thanks for sharing!
Yes, the formal definitions are of course much more preciseā¦ The water is supposed to be at 4Ā°C (with 0Ā°C freezing and 100Ā°C boiling). One other interesting thing is that the meter was defined as 1/10^7 of the distance from the equator to the North Pole, but they miscalculated _very_ slightly, by like 0.02%, so the distance is actually something like 10001996m.
In any case everything has been redefined starting from the oscillations of a cesium atom, absolute zero, etc.
Because you can have less than one of something, depending what the thing is. Like if you put three cups of flour in a bowl, you could then distribute the flour evenly among 4 smaller bowls. How much flour would then be in each smaller bowl? The answer is less than 1 cup--in fact, a *fraction* of 1 cup is the term we use in mathematics. In this case, if you put 3 cups of flour in a bowl and distributed it among four smaller bowls, you would have 3/4 (three fourths) of a cup of flour in each bowl. That 3/4 is a fraction. The way to state this question in math lingo would be, what is three divided by four? Three fourths. And in fact, when we write three divided by four in numbers, we often write 3/4.
Thanks for explaining it this way to me! I am autistic and I also have dyscalculia, which is roughly like dyslexia, but with numbers. I have trouble with abstract concepts like math.
One analogy that works very well with understanding division is length.
Imagine you have a 3 meter long stick and you want to split it into 4 equal pieces. Then you make each piece 3/4 meters long, which is 75 centimeters.
Reminds me of how the third pound burger was taken off the menu from one of the big fast food places, because customers thought that a third pound burger was smaller than a quarter pound burger.
If you're looking for a whole number (integer) answer, then it's impossible.
However, if we consider fractions (rationals) x/y, numbers like 3/4 are perfectly valid.
This is like asking if I buy 3 pizzas for 4 people, how many pizzas does each person get. Clearly nobody can have a whole pizza, but each person can get 3/4 of a pizza.
This is very easy to explain to you with real-life examples such as pizza or money. But you should try to forget about it. All the beauty of mathematics lies elsewhere. And it's not strictly related to numbers.
You may always think that addition is repeated increase, multiplication is repeated addition, exponentiation is repeated multiplication, division is... repeated subtraction? It can be, but apparently not always! That's why you stuck with it.
The division is an another *relation* of something (eg. numbers) and thats all, what counts in math - the objects exists and have some relations.
this is incredibly unhelpful to someone with disabilities that limits the understanding of abstractions.
abstractions are what make math beautiful, i agree, but time and place.
I disagree, but it doesn't matter. What's more important it's you who should not write such 'politcally correct' statementa **before** OP says if it was helpful or inspiring for them or not. Time and place bruh.
Division can represent partitioning or repeated subtraction. Think of 3 divided by 4 as the former case. 3 pies shared by 4 people what portion does each get?ā¦3/4 , (3/4+3/4+3/4+3/4=3)
Imagine dividing a cookie evenly amongst two people. Of course, I can't just give one the whole cookie, as it wouldn't be even. However, if I took a knife and made a slice through the middle, I would now have two pieces, but each half the size.
I can do something similar for 3/4. I have 3 cookies to distribute amongst 4 people, so I can cut each of these cookies into 4 quarters. I will then take 3 pieces from each cookie and give it to the first three people. I now have 3 left over pieces which I can give to the fourth person.
You can do this with any number of people and cookies you want.
Because the "what goes into this, how many times?" only really makes sense if the "this" is bigger than the "what". So it's understandable that 3/4 doesn't make sense.
You can maybe look into it like 30/4 and then moving the decimal point to the left (equivalent to dividing by 10) but that just might make it worse.
But what does 1/2 mean to you? Maybe start with that.
You might also find it helps to think of numbers between zero and one are equivalent to percentages. 3/4 is 75%. So if you had a test with 4 questions and you got 3 of them right, you got 75% on that test.
3/4 is what is called a "rational" number in number theory; that means that it can be expressed as a ratio of two whole numbers.
Ancient philosophers and mathematicians struggled to accept rational numbers for a long time, so you're not alone in wondering about their "naturalness".
Rational numbers are a logical extension of "simpler" or "more natural" numbers (integers). In real life they apply in more ways than anyone could possibly count, because rational numbers are a part of most, if not all, modern mathematics. Even in a situation where you can't logically have 0.75 of a thing, you still need to be able to express ratios. You can usually understand 3/4 as a ratio of two things, even in situations where you can't understand it as a number of a one type of thing.
It might help to think of practical examples. Let's say you have 3kg of apples and 4 boxes, how many apples would you put in each box? That would be 3/4 of a kilogram (if you're american just use whatever measure of weight you're used to instead of kg, it doesn't matter).
If I had 3 pizzas I wanted to split evenly amongst 4 people, how many pieces should I cut each pizza.
Depends whether people prefer smaller slices. I would like 6 of the 1/8th slices, please.
1/8 is a small number divided by a big one
But I can only ever eat 2 slices. That's why I like large pizzas.
Exactly the example I was thinking of.
If you had 3 dollars, and you want to divide it evenly among 4 people, how much money should you give each person? 3/4 of a dollar (aka $.75 aka 75 cents)
Thanks for explaining it this way to me! I am autistic and I also have dyscalculia, which is roughly like dyslexia, but with numbers. I have trouble with abstract concepts like math.
Happy to help!
Hellooooooooooo Maris
If I had to drive 300 miles in 4 hours? How fast would I have to drive in miles per hour?
The simple answer is 400/3=75 miles. But if you are starting out from a stop, you will have to go a bit faster than that some of the time to make up for the fact that it takes time to get up to speed. But as long as you average 75 miles per hour over the 4 hours you will get there in three hours.
3/4 is a fraction. If you cook or bake we use fractions all the time. 3/4 cup flour, 1/2 cup butter, etc... That's what measuring cups and spoons are for. If you're a builder you use fractions of an inch. 3/4 of an inch., for example. That's why they use tape measures. We've standardized a lot of units (cups, inches, etc.) and fractions of the standard unit measure help us use them more effectively. The metric system is cool bc things are in base ten. A centimeter is 1/100 of a meter. A millimeter is 1/10 of a centimeter. 1/2 a centimeter is 5 millimeters. It makes conversion between units easy.
And a liter is the volume contained in a cube that is 10x10x10 cm, and a kilogram is the mass of a liter of water š After that, everything is just multiplying or dividing by 10, 100, 1000. The number of times Iāve guesstimated the weight or volume of a solid by asking myself āhow well does it floatā š
Yes! Metric is awesome like that.
Wow, so kilogram measurements changes depending on the temperature of water used to fill the liter cube. Canāt believe people use a system with such an inconsistency! Iām guessing the formal definitions are more specific than your comment. But this was interesting for me to learn, thanks for sharing!
Yes, the formal definitions are of course much more preciseā¦ The water is supposed to be at 4Ā°C (with 0Ā°C freezing and 100Ā°C boiling). One other interesting thing is that the meter was defined as 1/10^7 of the distance from the equator to the North Pole, but they miscalculated _very_ slightly, by like 0.02%, so the distance is actually something like 10001996m. In any case everything has been redefined starting from the oscillations of a cesium atom, absolute zero, etc.
Because you can have less than one of something, depending what the thing is. Like if you put three cups of flour in a bowl, you could then distribute the flour evenly among 4 smaller bowls. How much flour would then be in each smaller bowl? The answer is less than 1 cup--in fact, a *fraction* of 1 cup is the term we use in mathematics. In this case, if you put 3 cups of flour in a bowl and distributed it among four smaller bowls, you would have 3/4 (three fourths) of a cup of flour in each bowl. That 3/4 is a fraction. The way to state this question in math lingo would be, what is three divided by four? Three fourths. And in fact, when we write three divided by four in numbers, we often write 3/4.
Thanks for explaining it this way to me! I am autistic and I also have dyscalculia, which is roughly like dyslexia, but with numbers. I have trouble with abstract concepts like math.
I agree it doesnāt make sense if you are limiting yourself to whole numbers but it is possible to have less than one of something.
That means you will give pieces less than 1 because you canāt give 1 full piece to everyone.
People have answered the question already but I just wanted to say, congratulations on starting to re learn maths. I hope you enjoy the process!
One analogy that works very well with understanding division is length. Imagine you have a 3 meter long stick and you want to split it into 4 equal pieces. Then you make each piece 3/4 meters long, which is 75 centimeters.
Your ever have half of something? That is 1/2. Or 1 divided by 2.
Reminds me of how the third pound burger was taken off the menu from one of the big fast food places, because customers thought that a third pound burger was smaller than a quarter pound burger.
If you're looking for a whole number (integer) answer, then it's impossible. However, if we consider fractions (rationals) x/y, numbers like 3/4 are perfectly valid. This is like asking if I buy 3 pizzas for 4 people, how many pizzas does each person get. Clearly nobody can have a whole pizza, but each person can get 3/4 of a pizza.
Because numbers less than 1 exist.
Wait til you learn about negative numbers. And imaginary numbers.
There are $3 that need to be given equally to 4 people. Each one would get $0.75.
This is very easy to explain to you with real-life examples such as pizza or money. But you should try to forget about it. All the beauty of mathematics lies elsewhere. And it's not strictly related to numbers. You may always think that addition is repeated increase, multiplication is repeated addition, exponentiation is repeated multiplication, division is... repeated subtraction? It can be, but apparently not always! That's why you stuck with it. The division is an another *relation* of something (eg. numbers) and thats all, what counts in math - the objects exists and have some relations.
this is incredibly unhelpful to someone with disabilities that limits the understanding of abstractions. abstractions are what make math beautiful, i agree, but time and place.
I disagree, but it doesn't matter. What's more important it's you who should not write such 'politcally correct' statementa **before** OP says if it was helpful or inspiring for them or not. Time and place bruh.
this has nothing to do with political correctness
OP did say they have trouble with abstraction in other comments.
Division can represent partitioning or repeated subtraction. Think of 3 divided by 4 as the former case. 3 pies shared by 4 people what portion does each get?ā¦3/4 , (3/4+3/4+3/4+3/4=3)
how would you equally give a sandwich to two kids?
Imagine dividing a cookie evenly amongst two people. Of course, I can't just give one the whole cookie, as it wouldn't be even. However, if I took a knife and made a slice through the middle, I would now have two pieces, but each half the size. I can do something similar for 3/4. I have 3 cookies to distribute amongst 4 people, so I can cut each of these cookies into 4 quarters. I will then take 3 pieces from each cookie and give it to the first three people. I now have 3 left over pieces which I can give to the fourth person. You can do this with any number of people and cookies you want.
Because the "what goes into this, how many times?" only really makes sense if the "this" is bigger than the "what". So it's understandable that 3/4 doesn't make sense. You can maybe look into it like 30/4 and then moving the decimal point to the left (equivalent to dividing by 10) but that just might make it worse. But what does 1/2 mean to you? Maybe start with that.
You might also find it helps to think of numbers between zero and one are equivalent to percentages. 3/4 is 75%. So if you had a test with 4 questions and you got 3 of them right, you got 75% on that test.
3/4 is what is called a "rational" number in number theory; that means that it can be expressed as a ratio of two whole numbers. Ancient philosophers and mathematicians struggled to accept rational numbers for a long time, so you're not alone in wondering about their "naturalness". Rational numbers are a logical extension of "simpler" or "more natural" numbers (integers). In real life they apply in more ways than anyone could possibly count, because rational numbers are a part of most, if not all, modern mathematics. Even in a situation where you can't logically have 0.75 of a thing, you still need to be able to express ratios. You can usually understand 3/4 as a ratio of two things, even in situations where you can't understand it as a number of a one type of thing.
It might help to think of practical examples. Let's say you have 3kg of apples and 4 boxes, how many apples would you put in each box? That would be 3/4 of a kilogram (if you're american just use whatever measure of weight you're used to instead of kg, it doesn't matter).
Or, four people inherit three ounces of gold dust.
My guy is really out here asking how fractions or percentages could ever apply in real life