2+2=4 and 2x2=4,why?

Answer 1

Forget the signs.

Take four things. Arrange them in a square. You have two rows of two. Two times two makes 4. One row is two, the other row is two. Two plus two makes four. Get it?

Answer 2

2 + 2 = 4 because if you take two of something, add two more of the same thing, you end up with four of them.

Two apples + two apples = four apples.
Two oranges + two oranges = four oranges.

Two apples + two oranges = ... well, it's equal to two apples and two oranges. You can't say four apple-oranges... addition only works when you're adding the same type of item. If you want to skirt the issue and say two apples + two oranges = four pieces of fruit, that works because apples and oranges are each pieces of fruit; two pieces of fruit + two pieces of fruit = four pieces of fruit.

2 + 2 = 4. So, why does 2 × 2 = 4? Because of a definition of multiplication, that it's repetitive addition. In the addition fact 2 + 2 = 4, there are two addends of 2. That's why 2 × 2 = 4. If you take any number and add it to itself, you have two times that number.

So, 2 + 2 = 4, and 2 × 2 = 4. Are they the only pair of numbers that when added or multiplied yield the same sum as their product? Nope. Pick any number (except 1). Divide that by one less than the number you picked. The quotient and the number with which you started will give the same sum as its product.

First number: 2.
Second number 2 / (2 - 1) = 2 / 1 = 2.
2 + 2 = 4 and 2 × 2 = 4.

Want to try again?
First number: 3.
Second number: 3 / (3 - 1) = 3 / 2 = 1.5
3 + 1.5 = 4.5 and 3 × 1.5 = 4.5

One more?
First number: (-5 / 4).
Second number: (-5 / 4) / [(-5 / 4) - 1] = (-5 / 4) / (-9 / 4) = (5 / 9).
(-5 / 4) + (5 / 9) = (-25 / 36) and (-5 / 4) × (5 / 9) = (-25 / 36).

Why does this work?
First number: x.
Second number: x / (x - 1) = y.
xy = x[x / (x - 1)] = x² / (x - 1)
When you divide that, you get x + [x / (x - 1)], which is x + y. The product xy is equal to the sum x + y.

Because y is defined as a fraction x / (x - 1), most of the time you're going to have at least one fraction as one of your pairs whose sum = product. The only integer pairs for which this will work are:
2 and 2 (2 + 2 = 4, 2 × 2 = 4), or
0 and 0 (0 + 0 = 0, 0 × 0 = 0).

Answer 3

It's sort of a coincidence, but not entirely. What might make it clearer is to step back for a moment and think of the meaning of the numbers involved.

When we add, we're grouping like things together. Each number can be thought of as a quantity of some object. "If I have two apples, and you give me two apples, how many apples do I have?"

But when we multiply, the first number doesn't represent a quantity of objects, but instead a quantity of *groups* of objects. It represents the number of times I add something else together. "Two times 2" means that I'm adding two 2's together.

So ultimately the reason 2+2 and 2x2 come out the same is because, in 2+2, you are adding two 2's. That "two" is the first number in the multiplication.

Hope that made sense!

Answer 4

N + N = N X 2
if N = 2, then 2 + 2 = 2 X 2 = 4

Answer 5

Multiplication is defined by
0*x=0 (by definition)
(a+1)*x = a*x + x

setting a=0 we get
1*x = (0+1)*x= 0+x = x
Now you can set a=1:
2*x =(1+1)*x= x+x

Setting x=2 this reads
2*2 = 2+2

Now we only need to show that 2+2=4. The definition of 4 is
4 = 3+1
and the definition of 3 is
3= 2+1
So
4 = 2+1+1
But the definition of 2 is
2=1+1
so the previous equation reads
4=2+2

Wow! I've proved something today, first time for years!

Answer 6

well multiplying is basically adding. when u multiply 3x4, ur basically adding 3 four times. like 3+3+3+3. using multiplication is just a faster way of solving an addiction problem thats adding all the same numbers. and coincidentally, 2+2 is the same as 2x2.

Answer 7

because 2+2 = 2x2

Answer 8

coz 2+2 and 2x2 mean the same thing.
4

* * +**=4
@@x@@=4

Answer 9

Your question tickled me, so I through I would offer you a
short story, for fun.

Not to long ago I enrolled into a Modern Math Class, on the
second day, we were presented with: What is half of 8?
Ha, everyone knows that answer, but not so, the answer = 3,
because in Modern Math, the 8 gets sliced in half, lengthwise.

Have a Good Day!

Answer 10

Because 2*2 is just another way of saying 2 groups of 2.
As in, I have two apples in one hand, and two in the other, 2 groups of 2 makes four.

Answer 11

2X2or2+2
the double of one is 1+1=2
the double of two is 2+2=4
so 2*2=4 and 2+2 is equal to 4