### Can you add two irrational numbers to get a rational number?

Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive…

### Can you add an irrational number and a rational number?

Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.

### How is the sum of a rational and irrational number irrational?

This can easily be proved by contradiction. Without loss of generality, I will take specific numbers as an example. The proof can easily be extended to any rational + irrational number. Assumption: 1 plus the square root of 2 is rational. (It is a well-known fact that the square root of 2 is irrational. No need to prove it here; you can use any other irrational number will do.) This rational sum can be written…

### How do you prove that the sum of a rational number and its additive inverse is zero?

I can give you an example and prove it: eg. take the rational no. 2......hence its additive inverse ie. its opposite no. will be -2 now lets add: =(2)+(-2) =2-2 =0 it means that the opposite no.s. get cancelled and give the answer 0 this is the same case for sum of a rational no. and its opposite no. to be ZERO

### How to findout and write a rational number between 2 and 3?

A rational number is any number which can be expressed as the ratio of two integers (including the integers themselves in this definition). So any number which is more than 2 and less than 3, and which can also be expressed finitely, is a rational number. 2¼, 2½, 2¾ 2 plus any fraction (less than one) will fit your bill.

### Rational number between 3 and 4?

A rational number is any number that, when put into decimal form, terminates after a finite amount of digits OR begins to repeat the same pattern of digits. An easy way to find rational numbers is that any number that can be expressed in a fraction (1/2, 9/4, etc) of two integers.There is an infinite number of rational numbers between any two rational numbers. For example, say we have the numbers 1 and 2. What…

### Is a rational number a natural number?

A rational number is sometimes a natural number. For example, 7 would be a rational number and a natural number. But 7.25 is a rational number and not a natural number. A natural is the number 1 and any other number obtained by adding 1 to it repeatedly; either an element of the set {, , , ...} (the positive integers) or an element of the set {, 1, 2, 3, ...} (the non-negative integers)…

### Is the sum of two rational numbers sometimes 0?

Yes. For example: * 0 + 0 = 0 * 1/1 + (-1/1) = 0 * 1/2 + 1/3 is not equal to zero. If the second rational number is the additive inverse of the first, then yes the sum of two rational numbers can be zero. The additive inverse is that number when added to another number gives the result 0, and is denoted as the negative of the first number; the additive inverse…

### All rational numbers are integers?

A rational number is a number which can be expressed as the quotient of two integers, a quotient being the solution to a division sum. Therefore, 1/2, or one half, is a rational number, equal to 0.5. However, 1/3, or one third, is an irrational number, because if you had to write the number out as a decimal, the number would continue to recur. Therefore, all integers are rational numbers, but not all rational numbers…

### How many rational numbers can be put between 2 and7?

There are an infinite number of rational numbers between any two rational numbers. And 2 and 7 are rational numbers. Here's an example. Take 2 and 7 and find the number halfway between them: (2 + 7)/2 = 9/2, which is rational. Then you can take 9/2 and 2 and find a rational number halfway: 2 + 9/2 = 13/2, then divide by 2 = 13/4. No matter how close the rational numbers become, you…

### Why the sum difference and product of 2 rational numbers rational?

A rational number is one that can be expressed as a/b The sum of two rational numbers is: a/b + c/d =ad/bd + bc/bd =(ad+bc)/bd =e/f which is rational The difference of two rational numbers is: a/b - c/d =ab/bd - bc/bd =(ab-bc)/bd =e/f which is rational The product of two rational numbers is: (a/b)(c/d) =ac/bd =e/f which is rational