This may sound like a silly question but why does 2 x 2 = 4, and 2 + 2 = 4, yet 3 x 3 = 9, and 3 + 3 = 6.?

Question

I believe this to be a much more complicated mathematical question than it appears on the surface. But I have been trying to figure out other numbers where the sum of them is equal to the product of them. But I am stumped.

Thanks,

Answer 1

You said that you have been trying to figure out numbers where the sum of them is equal to their product. There are only two such real numbers 0 and 2.

x + x = x^2
x^2 - 2x = 0
x(x-2) = 0
x= 0 or 2

Answer 2

You're looking for two numbers whose sum is equal to their product?

x + y = xy
x - xy = -y
x(1 - y) = -y
x = -y / (1 - y)
x = y / (y - 1)

Substitute in any number for y (except 1)... solve for x in the equation
x = y / (y - 1), and you'll have a pair of numbers. (There are infinitely many of them.)

If y = 2, then x = 2 / (2 - 1) = 2 / 1 = 2.
2 + 2 = 4; 2 × 2 = 4.

If y = 0, then x = 0 / (0 - 1) = 0 / (-1) = 0.
0 + 0 = 0; 0 × 0 = 0.

If y = 3, then x = 3 / (3 - 1) = 3 / (2) = 1.5.
1.5 + 3 = 4.5; 1.5 × 3 = 4.5.

Try some negatives?
If y = -1, then x = (-1) / (-1 - 1) = -1 / (-2) = 0.5.
0.5 + (-1) = -0.5; 0.5 × (-1) = -0.5.

If y = -3, then x = (-3) / (-3 - 1) = -3 / (-4) = 0.75.
0.75 + (-3) = -2.25; 0.75 × (-3) = -2.25.

Try some fractions?
If y = (1/4), then x = (1/4) / (1/4 - 1) = (1/4) / (-3/4) = (-1/3).
(-1/3) + (1/4) = (-4/12) + (3/12) = (-1/12);
(-1/3) × (1/4) = (-1/12).

If y = (22/7), then x = (22/7) / (22/7 - 1) = (22/7) / (15/7) = (22/15).
(22/15) + (22/7) = (154/105) + (330/105) = (484/105);
(22/15) × (22/7) = (484/105).

Answer 3

An anomaly having to do with that particular number. mulitplication is just compound addition. a x b means a added b times so with 2 x 2 it is the same as 2 + 2. Probably has to do with the fact your dealing with 2 numbers. If you deal with any other number it changes 3 + 3 = 6 3 x 2 =6. 4 + 4 = 8. 4 x 2 =8. 8 + 8 = 16 8 x 2 = 16, (notice magic number 2) 3 + 3 +3 = the same as 3 * 3 (the number of numbers you are adding changes things) 4+4+4+ 4 = 16 = 4 x 4 = 16. Now if you understand all of that Your real name must be Albert Einstein, I don't .

Answer 4

Because 2 X 2 is like saying I have two twos. Two twos is the same as 2 plus 2.

3 x 3 is saying I have 3 threes.

Multiplication is a form of adding if you really think about it. We're just skipping a ton of steps.

3 x A is the same as A + A + A
5 x A is the same as A + A + A + A + A

The fact that 2 x 2 = 2 + 2 is the same goes for any number squared such that:

3 x 3 = 3 + 3 + 3
4 x 4 = 4 + 4 + 4 + 4
5 x 5 = 5 + 5 + 5 + 5 + 5

and so on.

You justed stumbled on the first pattern. Its not so much as its a pattern, its the standard definition of multiplication and sqauring.

Hopefully that answers your question... its not as mind-blowing as you may have originally thought but there it is.

Answer 5

First of all, don't bother looking for other numbers where the sum is equal to the square (the number times itself). You've already found it; 2 is the only number this works for. The reason is that two times two is 2 + 2, which equals four. Basically, saying 2 * 2 is the exact same thing as 2 + 2. The reason it doesn't work for other numbers, say 3 * 3, is becasue 3 * 3 is equivalent to 3 + 3 + 3, which is nine, where as 3 + 3 is, obviously six. If you want to keep at it, more power to you, but simply put, it isn't possible for any number other than two.

Answer 6

well............. 2 x 2 = 4 and 2 +2 = 4 bc we all know 2 + 2 = 4 .......... 2 x 2 = 4 bc if you wrote this out as an addition problem it would be like this.... 2 + 2 = 4 just like the one above 3 + 3 = 6 we all know why but 3 x 3 = 9 bc if you it as an addition problem it would be 3 + 3 + 3 = 9 get it?? and i dont think that was a silly question lots of ppl have asked me that question before im just really good at math lol!!

Answer 7

Multiplication is just a shortcut to addition. 2x2 means two done twice, or 2+2. 3x3 means three done three times, or 3+3+3. It's not a pattern. It's a progression. There IS no other number where the sum equals the product. Oh, all right, there IS '0'.

Answer 8

To figure out other numbers where the sum of them is equal to the product of them, use algebra:

a+a=a^2 (a plus a equals a squared)
2a = a^2
0 = a^2 - 2a
0 = a(a-2)
0 = a, 0 = a-2
0 = a, 2 = a

Thus, the only 2 numbers where the sum of them is equal to the product of them are 0 and 2.

Answer 9

b/c 3 x 3 means 3 + 3 + 3 and 2 x 2 means 2 + 2

Answer 10

ok well i am 14 almsot 15 so here it goes basically u should have learned where the numbers come from a set or numbers 1-10 equal 1 yet not a complete set may range from 2-9 so therefore
its quite simple 2+2 is 4 and 2x2 is 4 y theey are smaller incriments of measurement therefore they do not equal much hope i could help

Answer 11

Why would you be stumped? 3 is larger in quantity than 2 AND 2 is a pair! 3 is the second odd number of the number table, after 1, a single. 'Mathematics has proved this with oranges." Expression.