112 is an integer and not a fraction. However, it can be expressed in rational form as 112/1. You can then calculate equivalent rational fractions if you multiply both, its numerator and denominator, by any non-zero integer.
"Integer" means "whole number". From everything you've told us, all we know about 'A' is that it's a whole number.
Yes, we can get a rational number on the addition of two irrational numbers.e.g. Let us consider two irrational numbers: 3 + √2 and 4 - √2.Addition yields:(3 + √2)+ (4 - √2) = 3 + 4 = 7(a rational number).Another example is:Addition of √2 and -√2.√2+ (-√2) = 0(a rational number).Explanation of example 1:Irrational numbers in the form of of p + q are are the irrational numbers which are obtained on addition of two terms: one is rational(p) and another is irrational(q).And on taking the conjugate of p + q we get p - q, which is an another irrational number. And the addition of these two yields a rational number.
We know that one of these numbers is a whole number, but we don't know what kind of number the other is, so this statement doesn't tell us anything. We can make different assumptions about the first number, though, and make conclusions that way.Let X be the first number of unknown type, and Y be the whole number, "whole number" meaning the subset {0, 1, 2, 3, …} of the integers. Then:if Y is an integer (any element of the set {…, -2, -1, 0, 1, 2, …}, then the product of X and Y is an integer.if X is a negative integer, the product of X and Y is a negative integer or 0 (which would happen when Y is 0).if X is 0, the product of X and Y is 0.if X is a non-integer rational number, and this rational number can be expressed with a denominator equal to Y, then the product of X and Y is the numerator of X. For example, if X is 20/4 and Y is 4, the product of the two is 20.You can make other rules like this for other situations.
fraction, a ratio of two integers p/q where q is not equal to zero.
Rational numbers are represented in the form of p/q , where p is an integer and q is not equal to 0.Every natural number, whole number and integer can be represented as rational number.For example take the case of integer -3, it can be represented in the form of p/q as -3/1 and q is not equal to zero, which means that rational numbers consist of counting numbers, whole numbers and integers.Now, what will be the result of product of any two rational numbers?Let us take the case of two rational numbers which are x/y & w/z, their product is equal toxw/yz, which is a rational number because multiplication of x and w results in an integer and also multiplication of y and z results in an integer which satisfies the property of rational numbers, which is in the form of p/q.So, product of any two rational numbers is a rational number.
To prove a number ab is rational, you have to find two integers t and n such that t/n = ab.Since we know that a, and b are rational, they can be expressed as follows:a = p1/q1b = p2/q2then ab = p1p2/q1q2Since p1, p2, q1, and q2 are all integers, p1p2 is an integer, and q1q2 is an integer. This gives us the t, and n we are looking for. t = p1p2 and n = q1q2, and ab = t/n, so ab is rational.
112 is an integer and not a fraction. However, it can be expressed in rational form as 112/1. You can then calculate equivalent rational fractions if you multiply both, its numerator and denominator, by any non-zero integer.
Yes. Not only that, but there are an infinite number of rationals between any two distinct rationals - however close. We can prove it like this: Take any three rational numbers, call them A, B and C, where B is larger than A, and C is any rational number greater than 1: D = A + (B - A) / C That gives us another rational number, D, no matter what the values of the original numbers are.
"Integer" means "whole number". From everything you've told us, all we know about 'A' is that it's a whole number.
We don't understand a number with two decimal points in it. If you mean the number that we would write with commas in the US: 2,247,000 then that number is rational.
True.
26 is an integer and not a fraction. However, it can be expressed in rational form as 26/1 which cannot be simplified.
an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.
Well, isn't that a happy little question! The rational number between 9 and 9.1 is 9.05. Just like adding a touch of color to a painting can bring it to life, finding that number between two others can help us see the beauty and harmony in mathematics. Just remember, there's no mistakes, just happy little accidents in learning.
There are infinite rational numbers between 2 and 3.Explanation:Let us write a few decimal numbers between 2 and 3: 2.01, 2.001, 2.0001,.., 2.4, 2.90 etc. Just change digits after the decimal point and this way we can write infinite decimal numbers between 2 and 3. And each decimal number can be expressed in the form of p/q(rational number)2.01 = 201/1002.001 = 2001/1000... 2.4 = 24/10 and so on.So there are infinitely many rational numbers b/w 2 and 3.
Yes, we can get a rational number on the addition of two irrational numbers.e.g. Let us consider two irrational numbers: 3 + √2 and 4 - √2.Addition yields:(3 + √2)+ (4 - √2) = 3 + 4 = 7(a rational number).Another example is:Addition of √2 and -√2.√2+ (-√2) = 0(a rational number).Explanation of example 1:Irrational numbers in the form of of p + q are are the irrational numbers which are obtained on addition of two terms: one is rational(p) and another is irrational(q).And on taking the conjugate of p + q we get p - q, which is an another irrational number. And the addition of these two yields a rational number.