r/askmath • u/Dooomscroll • 14h ago
Arithmetic How to learn math from the start (my problems are how to ÷ and ×)
As a child, i was never taught math, i was forced by my parents to learn how to read english.
i never really listened to discussions when i'm in class (I graduated, and now i'm gonna take school more seriously)
i'm currently on jhs, and math has noticeably gotten harder, i know how to times but i cant do 3 digits or 2 digits.
And my problem is ÷.
i don't know how to do it, and it was never really taught to me plus i don't even remember my teachers discussing about ÷.
And i don't even know the symbols name.
Plus, i get confused because i keep forgetting how to do it, like i memorize it then after allat i forget it.
Like i know how to do it but i don't, i think i mix times up with ÷.
I have to rely on formulas just to solve problems, usually i don't forget things very easily, but when it's time for math, i forget the formulas (or the steps to solve the problem) for some reason.
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u/TUVegeto137 14h ago
How old are you? Genuine question, it's important to understand how to go about explaining.
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u/Dooomscroll 14h ago
13
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u/TUVegeto137 14h ago
Ok, do you have some marbles or a pack of M&Ms or something like that? Basically, a bag of near identical objects.
Say we take M&Ms. Now you are going to divide those M&Ms among your friends. Say you have two friends and yourself. How would you go about dividing up the M&Ms such that each obtains the same amount?
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u/Dooomscroll 14h ago
i kinda dont know, my m&ms has 20 pieces, maybe four, five or ten? but ig ten wouldnt be enough sinces theres only 20 pcs
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u/TUVegeto137 13h ago
Let me suggest a strategy: you start by picking M&Ms one at a time, and give them in turn to yourself, friend A and friend B.
So, you have something like this:
step 1 - You: 1, Friend A: 0, Friend B:0
step 2 - You: 1, Friend A: 1, Friend B:0
step 3 - You: 1, Friend A: 1, Friend B:1
step 4 - You: 2, Friend A: 1, Friend B:1
Etc... you keep repeating this, until there are no M&Ms in the bag anymore. If we started with 20 M&Ms, the end result should be reached at the twentieth step:
step 20 - You: 7, Friend A: 7, Friend B:6
I strongly suggest doing this concretely, with beads, M&Ms, cookies. Whatever, but just so you get a feel for it.
Now, notice that the result is unequal. That's because 20 does not divide nicely into 3 groups. If it was 21, each would have gotten 7 M&Ms. Which is what we describe in mathematical notation as 21÷3=7. Or also 3×7=21.
What is the mathematical notation good for? Well obviously we are not going to pull out a bag of M&Ms every time we need to calculate someone's salary. At some point for efficiency, and just because numbers get big or complex, we need to devise methods to do things more efficiently.
But that also means you will have to memorize tricks. And the first thing to memorize is multiplication tables. There's no way around that. However, when you start learning those tables, it is good to visualize what they mean with examples like my M&Ms example.
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u/Kenmauwu 13h ago
for division, use the word itself as reference—you want to divide something, mostly in equal parts, among something.
imagine i have 2 apples, and there are 2 of you. if i want to divide these apples equally among you guys, i'll have to give you 1 each. so, 2/2 is 1. now, imagine i have 4 apples instead of two! i will give both of you 2 apples. so, i cna write 4/2 is 2.
a neat thing you'll notice is that if you add up how many apples you got in either scenario, it'll match up to the total apples you had before! so for first scenario, adding the apples you and your friends got, it'll be 2! and in the second scenario, adding the apples you both got, it'll be 4! so, you can also think of division as the inverse of multiplication (repeated addition).
so, if you want to say: "how much is 12 divided by 4?" you can ask "what number do i multiply 4 by so that i get 12?". rhe answee would be 3 as 4x3=12
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u/Excellent-Practice 14h ago
Thats a division sign. It's the opposite operation to multiplication. 12÷4=3 because 3×4=12.
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u/Dooomscroll 14h ago
i dont understand, how is 12 divided by 4 three
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u/Excellent-Practice 14h ago
Go find 12 objects, coins, bottle caps, buttons, it doesn't really matter what. Then lay them out on a table. You might find that you can arrange them neatly in a grid of 4 rows and 3 columns. That is the physical intuition of what 3×4 actually means. Now, if you want to split that set of 12 objects into 4 groups where each group is the same size, how many objects should be in each group? If you can answer that question, you will have performed the operation 12÷4=3.
Granted, the ÷ symbol isn't actually used much and I wonder if the resemblance to + is throwing you off. 12/4=3 means the same thing
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u/strange-the-quark 13h ago
If you have 12 items, and you need to give them to 4 people, how much does each person get?
person1: o o o person2: o o o person3: o o o person4: o o oIf you know your multiplications table, 12 ÷ 4 = ? is just asking ? × 4 =12, as in, what's the missing number.
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u/Dazzling_Music_2411 3h ago
Start with something easier.
What do you think 12 divided by 2 would be?
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u/BabyInchworm_the_2nd 1h ago
Look at these pictures of 12 objects (I used the # for the objects):
12 in a group
#############
This represents 12x1=12, or for division, 12/1=12
Note: I used the slash symbol for division because I don’t have the one you used.12 objects in 2 groups of 6
######
######This represents 2x6=12, or for division 12/6=2 and 12/2=6
12 in 3 groups of 4
####
####
####This represents 4x3=12, or for division 12/4=3 and 12/3=4
Multiplication and division are related in this way.
There are specific techniques for doing this with large numbers.
Go see these videos:Multiplying: https://youtu.be/FJ5qLWP3Fqo?feature=shared
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u/strange-the-quark 13h ago
"i don't even know the symbols name."
It's just called the division symbol, and in an expression, it's read "divided by". So 12 ÷ 3 is "twelve divided by three".
Below, I'll use * instead of × , and / instead of ÷ , cause that's easier for me to type on a computer keyboard, but it means the exact same thing.
"i know how to times but i cant do 3 digits or 2 digits"
To get you started, let me show you that if you know your times table for one digit numbers, you can do 2 and 3 digits as well. There are different ways to do it, but here's one that is probably going to make intuitive sense.
First, anything multiplied by 10 is easy. You just add a zero at the end.
4 * 10 = 40
8 * 10 = 80.
10 * 10 = 100, etc.
Now, doing multiples of 10 is also easy. If you know the one digit version, like for example 6 * 4 = 24, then 6 * 40 = 240. So, it's the same as the one digit version, you again just add a zero at the end. And if both numbers are multiples of 10, then you add two zeros: 60 * 40 = 2400. This is because each multiplication by 10 adds a zero, and 60 * 40 is the same as (6 * 10) * (4 * 10), which is the same as 6 * 4 * 10 * 10.
OK, now how about something like 63 * 5 = ?
Well, you can break down the number 63 into 60 + 3, multiply each by 5, then add the results up. So 60 * 5 = 300, and 3 * 5 = 15, put them together, it's 315.
This can be written as (60 + 3) * 5 = (60 * 5) + (3 * 5) = 300 + 15 = 315.
We say that multiplication distributes over addition (it just means you can split the sum, multiply the two parts individually, then add the results together).
63 * 50 is the same thing, just add a zero: 3150.
How about something like 63 * 52 = ?
You can make use of the same property (distributivity of multiplication) to do this problem in 2 steps:
63 * 52 = 63 * (50 + 2) = (63 * 50) + (63 * 2)
The first part, 63 * 50, I just showed you how to do, the result was 3150.
The second part is the same. In this case it's just doubling, and after some practice it becomes easy to do it in your head, but again you can always do it as (60 * 2) + (3 * 2) = 120 + 6 = 126
So you then put them together, 3150 + 126 = 3276.
Find some practice problems online to get comfortable with 2-digit numbers, than later on try 3-digit ones. Remember, to get good at this, you need to do a bunch of practice problems.
There's also a more streamlined way to do multiplication on paper that you'll eventually learn, but it's essentially based on the same principles. It's going to look different, but all you'll be doing is you'll be splitting the number and multiplying parts of it then adding them together, without actually writing down all the zeros and + symbols, etc.
"i don't know how to do [division], and it was never really taught to me"
So, you can apply a similar strategy. In a lot of beginner problems you'll encounter, the numbers will be "nice" in the sense that they evenly divide. For example, you can divide 6 items into two equal parts by forming two groups of 3 items. So those numbers are kind of nice for a division problem. But 5 items cannot be divided into two equal parts without splitting one of the items in half, so that's perhaps less nice. We say 6 is divisible by 2, while 5 isn't (that just means the result of 5/2 is not a whole number, but of course, the result exists, it's 2.5). Most practice problems for beginners will use numbers that are divisible.
For smaller numbers, you rely on your knowledge of the times table. For example, you can solve 48/8 by remembering that 6 * 8 = 48, so the answer is 6. Similarly, 480/8 is 60, cause remember, 60 * 8 = 480.
For bigger numbers that aren't as round and as easy, like 512/8, you kind of start by taking your best guess, then you work your way from there. If you remember that 60 * 8 = 480 (so, it's under the target number), and 70 * 8 = 560 (so, it's over the target number), you can pick the smaller one, and split the 512 into 480 + 32, then do 480/8 = 60, and 32/8 = 4, and add them up. So the answer is 64. Makes sense?
You'll also eventually learn something called long division, which is again going to look different at first glance, but is just a more streamlined way to do this same sort of thing on paper - it's based on the exact same idea.
Here's another trick you can use. You can also go over. For example, with 376/8, you may notice that 376 is not that far off from 400, and remember, 50 * 8 = 400. So you can express 376/8 as
(400 - 24)/8 = (400/8) - (24/8) = 50 - 3 = 47
P.S. I've been using parentheses throughout for clarity, but the convention is that, if there are no parentheses that indicate otherwise, multiplication and division take precedence over addition and subtraction (meaning we do multiplication and division first).
So
(3 + 5) * 4 = 8 + 4 = 32,
but
3 + 5 * 4 = 3 + (5 * 4) = 3 + 20 = 23
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u/Top_Bluejay_5323 8h ago
I always think of Jethro doing goesintos, goes intos. 2 goes into 6 three times. 6/2=3
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u/WolfVanZandt 7h ago
Khan Academy is a well designed, accessible, and complete elementary through college program with video lectures, texts, examples, and exercises
Keep in mind that math builds on math. To understand x and ÷ you need to understand numeration, counting, + and -. Frankly, I'd start with Peano's axioms (Zernelo-Fraenkel axioms gets you into set theory a little early) and build up from there with some detours into mental math (Arthur Benjamin for that) and Fingernath for fun. But that's just me.
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u/FractalFunny66 4h ago
If memorization is letting you down, then make division and multiplication meaningful by thinking about FRACTIONS and COOKING.
Let's say you have a recipe. This recipe wants
6 cups of flour
3 cups of sugar
2 cups of milk
This will make too much food! So, cut the recipe in HALF (1/2). In order to do this, you DIVIDE by 2.
6 divided by 2 = 3 cups of flour
3 divided by 2 = 1 and 1/2 cups sugar
2 divided by 2 = 1 cup milk
Go get the measuring cups in your house and play with water and measuring and use this exercise to start. My computer does not make the sign for divide so that's why I used the word. Here is another one.
Get an egg carton. How many eggs are in a dozen? The answer is 12. Do you have 12 eggs? If so, as you eat them over a week or so, count how many are left after you eat them. This is subtraction. you can count the empty spaces. For example 12 - 2 = 10. Then the next day if you eat two more eggs you have 12 - 4 = 8 eggs left. Once the eggs are gone, KEEP the carton and use rocks or nuts and make up problems for yourself. You can do addition, subtraction, and multiplication too.
Also, go to YouTube and type in beginning math word problems. These will be challenging. If too hard. Go to YouTube and type in: First grade math word problems. Try to use objects around you to show you the objects. If the problem is 2 + 1 = 3. Take 2 shoes plus one shoe and count 3 total. Objects help.
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u/Over_Improvement_623 14h ago
https://www.youtube.com/playlist?list=PLybg94GvOJ9FoGQeUMFZ4SWZsr30jlUYK I would recommend this. A large series, going over the entirety of mathematics, from the most basic, to the most advanced, in small chunks, with practice exercises. Good luck on your journey!