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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
Cross multiply:
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

Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:

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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

* Difference of Squares

* Sum of Cubes

* Difference of Cubes

* Binomial Expansions

* Quadratics

* 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

Irrational Numbers Between

Free Irrational Numbers Between Calculator - 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.
[MEDIA=youtube]tXoo9-8Ewq8[/MEDIA][/B]

Prove the sum of any two rational numbers is rational

Take two integers, r and s.
We can write r as a/b for integers a and b since a rational number can be written as a quotient of integers
We can write s as c/d for integers c and d since a rational number can be written as a quotient of integers
Add r and s:
r + s = a/b + c/d
With a common denominator bd, we have:
r + s = (ad + bc)/bd
Because a, b, c, and d are integers, ad + bc is an integer since rational numbers are closed under addition and multiplication.
Since b and d are non-zero integers, bd is a non-zero integer.
Since we have the quotient of 2 integers, r + s is a rational number.
[MEDIA=youtube]0ugZSICt_bQ[/MEDIA]

Rational Number Subtraction

Free Rational Number Subtraction Calculator - Subtracting 2 numbers, this shows an equivalent operations is adding the additive inverse. p - q = p + (-q)

Rational Numbers

Free Rational Numbers Calculator - 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

Free Rational Numbers Between Calculator - This calculator determines all rational numbers between two numbers

Rational,Irrational,Natural,Integer Property

Free Rational,Irrational,Natural,Integer Property Calculator - This calculator takes a number, decimal, or square root, and checks to see if it has any of the following properties:

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* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

* 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 Integer Test Natural Number Test

X is such that X belongs to rational numbers and X is less than or equal to 1 and greater than 0

X is such that X belongs to rational numbers and X is less than or equal to 1 and greater than 0
Greater than 0 means we don't include 0
0 <
less than or equal to 1 means we include 1:
[B]0 < x <= 1[/B]