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rational number - a number that can be expressed as the quotient or fraction p/q of two integers
A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you ge
A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number?
Let the rational number be x. We're given:
7x/3 - 3/2 = 92
Using a common denominator of 3*2 = 6, we rewrite this as:
14x/6 - 9/6 = 92
(14x - 9)/6 = 92
14x - 9 = 92 * 6
14x - 9 = 552
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]40.07[/B]
Factoring and Root Finding
This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
* Binomial Expansions
* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs
Irrational Numbers Between
This calculator determines all irrational numbers between two numbers
Prove sqrt(2) is irrational
Use proof by contradiction. Assume sqrt(2) is rational.
This means that sqrt(2) = p/q for some integers p and q, with q <>0.
We assume p and q are in lowest terms.
Square both side and we get:
2 = p^2/q^2
p^2 = 2q^2
This means p^2 must be an even number which means p is also even since the square of an odd number is odd.
So we have p = 2k for some integer k. From this, it follows that:
2q^2 = p^2 = (2k)^2 = 4k^2
2q^2 = 4k^2
q^2 = 2k^2
q^2 is also even, therefore q must be even.
So both p and q are even.
This contradicts are assumption that p and q were in lowest terms.
So sqrt(2) [B]cannot be rational.
This lesson walks you through what rational numbers are, how to write rational numbers, rational number notation, and what's included in rational numbers
Rational Numbers Between
This calculator determines all rational numbers between two numbers
This calculator takes a number, decimal, or square root, and checks to see if it has any of the following properties:
* Integer Numbers
* Natural Numbers
* Rational Numbers
* Irrational Numbers
Handles questions like:
Irrational or rational numbers
Rational or irrational numbers
rational and irrational numbers
Rational number test
Irrational number test
Natural Number Test