# how is 2+2 and 2×2 both equal 4?

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3+3 and 3×3 isnt the same, and the same thing with all other numbers. i don’t understand how 2+2 and 2×2 both equal 4

In: Mathematics

Multiplication can always be reduced to addition, iE 2×2 can be reduced to 2+2, 3×3 can be reduced to 3+3+3, 4×4 can be reduced to 4+4+4+4, stuff like 3×7 can also be reduced to 7+7+7 or 3+3+3+3+3+3+3

It’s just the way the math works out.

If you have 2 books, and then you get 2 more books you have 4 books.

But if you have 2 groups of 2 books… well that is exactly the same as what you had above so you have 4 books still.

It doesn’t work like that for any other numbers because it isn’t the same thing.

3*3 isn’t 3+3, but it is 3+3+3. 3 groups of 3.

The word plus is also the word “And.” 2+2 is also 2 and 2.

Multiplying is, “This number, that many times.” The number 2, 2 times = 2×2.

2 x 2 = 2 and 2, The same as the addition.

Now let’s look at it with 3.
**3 + 3** is **3 and 3.3 x 3** is **3 and 3 and 3.**

1×1 = 1
2×2 = 2+2
3×3 = 3+3+3
4×4 = 4+4+4+4
5×5 = 5+5+5+5+5

And so on. That’s why only two equals the same when added and multiplied.

A number plus itself is equal to a number times itself?

x + x = x * x

Looks like algebra!

2x = x^2

subtract 2x from both sides:

0 = x^2 – 2x

factor

0 = x(x-2)

So. either x is 0 or x is 2

0 + 0 = 0 * 0 = 0
2 + 2 = 2 * 2 = 4

… checks out!

Because 2+2 and 2×2 both happen to mean the same thing: you have two groups of two.

3+3 and 3×3 aren’t the same thing because the first is two groups of three and the second is three groups of three.

2 isn’t the only number this works for, either.

It works for 0 (0 + 0 = 0x0. Two groups of nothing is the same as having no groups of nothing; it’s still nothing).

It’s because + and &times; are both binary operators, which is to say, they each operate on two numbers. So using the number 2 has this special property. It even continues with exponentiation (though that doesn’t even have a visible operator): 2^(2)=4. If there were yet-higher-order binary operators in the same sequence then providing 2 as the operands would always give the answer 4.

Multiplication is just a fancy way to add. The reason why 3+3 isn’t the same as 3×3 is because 3×3 is the same as adding the number 3 three times. 3+3+3. So 2+2=4 and 2×2 is the same as saying 2+2 so it equals 4 as well.

In the same note division is a fancy way to subtract. 6/2 means that you count the number of times you can subtract 2 from six. So 6-2=4, 4-2=2, and 2-2=0, and we are done. So 6/2=3. This also explains why you can’t divide by 0. 6/0 means you need to count the number of times you can subtract 0 from 6. 6-0=6, 6-0=6, 6-0=6, and on and on.