Table of Contents
What topic of math is fractions?
fraction, In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
What is the point of continued fractions?
The continued fraction expansion of a real number x is a very efficient process for finding the best rational approximations of x. Moreover, continued fractions are a very versatile tool for solving problems related with movements involving two different periods.
What is a fraction for Class 7?
Fractions are numbers representing part of a whole. A fraction is a number of the form p/q, such that q is not equal to zero or one. A fraction has two parts. The number on the top is numerator and the number below is the denominator.
Who created continued fractions?
The Dutch mathematician and astronomer Christiaan Huygens (1629-1695) was the first to demonstrate a practical application of continued fractions. [6][5] He wrote a paper explaining how to use the convergents of a continued fraction to find the best rational approximations for gear ratios.
What is unlike fraction?
Unlike fractions are fractions that have different denominators. Examples. The first fraction below has a denominator of two and the second fraction below has a denominator of three. Since the denominators are different, they are unlike fractions.
What is fraction in maths for Class 8?
The fraction has two parts one is numerator and another denominator. The value which is present above the line is called a numerator and the value which is present below the line is known as a denominator. Proper fraction: The fraction where the value of numerator less than the value of denominator.
How many types of continued fractions are there?
There are two types of continued fractions: infinite continued fractions. a 0, a 1, … b 1, b 2, … n \\geq 1 n ≥ 1 . a 0, a 1, … b 1, b 2, … ,… are integers. An infinite continued fraction representation of a real number is in some ways analogous to its decimal expansion.
Why study the history of continuing fractions?
Those who wish to study a particular field of mathematics, whether it be statistics, abstract algebra, or continued fractions, will first need to study their field’s past. In doing so, one is able to build upon past accomplishments rather than repeating them. The origin of continued fractions is hard to pinpoint.
How do you reverse a continued fraction?
As with rational numbers, this process can be reversed. as a simple continued fraction. The idea is to iterate the process of taking the greatest integer and reciprocating, as follows: and the process repeats. These examples motivate the following theorem about periodic continued fractions. r = [ a 0; a 1, a 2, …]
Is a finite simple continued fraction a rational number?
As noted above, a finite simple continued fraction is a rational number. The converse is also true, i.e. any rational number r. r. r. Here is an illustrative example. to a simple continued fraction. − 551 = 802 ( − 1) + 251 802 = 251 ⋅ 3 + 49 251 = 49 ⋅ 5 + 6 49 = 6 ⋅ 8 + 1 6 = 1 ⋅ 6 + 0.