How could 2+2=10? or 2+2=11, as well as 2+2=4? Help!!!?

Question

So are teacher in communications wants the class to find out on there own how 2+2=10 just as 2+2=4.

He told us it represents how we can't believe everything as we are told

and he also told us any mathmatician would say that his concept is right.

he told us to think of are hands.

any ideas?

no 2 hands and 2 hands equals 20 fingers

Answer 1

2 + 2 = 4 is correct.

Since 4 is 10 in base 4, "2 + 2 = 10" is correct in base 4.

Likewise, "2 + 2 = 11" is correct in base 3, since 11 base 3 = 4 in our regular decimal base.

So, your prof is quite correct, and any three-fingered or four-fingered (and one handed) aliens would agree.:)

Answer 2

They all have something to do with what is known as "base representation of integers" (known also as radix) in mathematics.

In base-10 notation, which is also known as decimal notation, any (integer) number could always be represented by a combination of the following numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

So, when we said 2+2=4, we are actually talking about this decimal notation.

But, in base-4 notation, the available numbers are only 0, 1, 2, and 3. Because there is no "4" in base-4 notation, the representation of any number bigger than 3 is obtained by keep dividing the integer with 4 until what left is either 0, 1, 2 or 3.

The integer "4" in decimal notation, is then represented as 10 in base-4 notation, because 4 divided by 4 gives a "1" and without anything left (the rest of the division is a "0"). In other words, in base-4 notation, the integer "4" in decimal notation is represented by "10".

Meanwhile, in base-3 notation, what available are the numbers 0, 1, and 2. Here any number bigger than 2 should be divided by 3 until what left is either 0, 1, or 2. When we divide the number "4" with 3, we get "1" and the rest is "1". So what we know as the number "4" in decimal notation is represented by the "11" in base-3 notation.

Answer 3

The key to answering this question is to ask: "Two WHAT plus two WHAT equals ten WHAT"?

I don't know if "any" mathematician would agree with your teacher, but thinking about "our" hands, I dubiously see he's right for the same reason 2 + 2 = 2 X 2. Counting each hand, you'd come up with five fingers each, one palm each, and five knuckles each. Each finger has two joints, and the thumb has one; to even things out, its second joint would be where it joins your hand.

I hope this is a good start; I think I have the answer and don't realize it, but I'd love to know what your teacher's talking about too.

Perhaps he's referring to the "hour" hands of a clock. Think of a wristwatch or a grandfather clock; when one hand is on the "two" position, the hand is opposite the "eight". Turn the clock upside down, and then the "eight" will be in the "two" position. From an observer's viewpoint, the clock will have hit the "two" position twice. But it hasn't, it's hit the "two" and the "eight" positions consecutively. And two plus eight (also the observer's two plus two) equals ten! So 2 + 2 = 2 + 8 = 10, and the crowd goes wild!

(Hey, I can dream.)

Answer 4

2 + 2 = 10 (base 4)

2 + 2 = 11 (base 3)

2 + 2 = 4 (base 10)

Answer 5

If you look at different bases it would work. Normally what we use is base 10, meaning the second digit (from the right) is the tens digit and the third digit is hundreds, etc. However, other bases are possible. In base 4, "10" would equal four, and "123" would equal twenty-seven in base 10. In base 4, 2+2 is indeed equal to 10.

In base 3, meanwhile, 2+2=11, as "11" would equal four in base 3 (4 is 3+1).

Answer 6

Set 2 + Set 2 = Set 10 if all the numbers in set 2 equal 5.
For example If Set 2 consists of 1 1 1 & 2, then Set 2 + Set 2 = 10.

Answer 7

Not sure. Sounds like he wants to drive the class crazy more than anything. We all know that 2+2 is NOT 11 and 2+2 is NOT 10. It obviously means something else. Search a few different math websites. Good luck!

Answer 8

Well, by telling you to "think of your hands" I think he is reminding you that we normally count in base 10 (0,1,2,3,4,5,6,7,8,9 as the digits) since we have 10 fingers.

However, there are other bases out there, such as base 4, where the digits are only 0,1,2,3, and so 2 + 2 = 10 base 4, where the "1" represents the 4s column. Similarly in base 3, 2+2 = 11.

Answer 9

In a "Base 4" numeric system, 2+2 would equal 10.
In a "Base 3" numeric system, 2+2 would equal 11.

Answer 10

the 2 IS 2 hands...which is 10 fingers.