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From Wikipedia

Mass energy equivalence - Wikipedia, the free encyclopedia

This mass decrease is also equivalent to the energy required to break up the ..... in which the protons and neutrons in atomic nuclei lose a small fraction...

File:Decimal-fraction equivalents--v0006.png - Wikipedia, the free ...


Unit fraction

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n. Examples are 1/1, 1/2, 1/3, 1/4 etc.

Elementary arithmetic

Multiplying any two unit fractions results in a product that is another unit fraction:

\frac1x \times \frac1y = \frac1{xy}.

However, adding, subtracting, or dividing two unit fractions produces a result that is generally not a unit fraction:

\frac1x + \frac1y = \frac{x+y}{xy}
\frac1x - \frac1y = \frac{y-x}{xy}
\frac1x \div \frac1y = \frac{y}{x}.

Modular arithmetic

Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime. Then, by using the extended Euclidean algorithm for greatest common divisors we may find a and b such that

\displaystyle ax + by = 1,

from which it follows that

\displaystyle ax \equiv 1 \pmod y,

or equivalently

a \equiv \frac1x \pmod y.

Thus, to divide by x (modulo y) we need merely instead multiply by a.

Finite sums of unit fractions

Any positive rational number can be written as the sum of unit fractions, in multiple ways. For example,


The ancient Egyptians used sums of distinct unit fractions in their notation for more general rational numbers, and so such sums are often called Egyptian fractions. There is still interest today in analyzing the methods used by the ancients to choose among the possible representations for a fractional number, and to calculate with such representations. The topic of Egyptian fractions has also seen interest in modern number theory; for instance, the Erdős–Graham conjecture and the Erdős–Straus conjecture concern sums of unit fractions, as does the definition of Ore's harmonic numbers.

In geometric group theory, triangle groups are classified into Euclidean, spherical, and hyperbolic cases according to whether an associated sum of unit fractions is equal to one, greater than one, or less than one respectively.

Series of unit fractions

Many well-known infinite series have terms that are unit fractions. These include:

  • The harmonic series, the sum of all positive unit fractions. This sum diverges, and its partial sums
closely approximate ln n + Î³ as n increases.

Matrices of unit fractions

The Hilbert matrix is the matrix with elements

B_{i,j} = \frac1{i+j-1}.

It has the unusual property that all elements in its inverse matrix are integers. Similarly, Richardson defined a matrix with elements

C_{i,j} = \frac1{F_{i+j-1}},

where Fi denotes the ith Fibonacci number. He calls this matrix the Filbert matrix and it has the same property of having an integer inverse.

Unit fractions in probability and statistics

In a uniform distribution on a discrete space, all probabilities are equal unit fractions. Due to the principle of indifference, probabilities of this form arise frequently in statistical calculations. Additionally, Zipf's law states that, for many observed phenomena involving the selection of items from an ordered sequence, the probability that the nth item is selected is proportional to the unit fraction 1/n.

Unit fractions in physics

The energy levels of the Bohr model of electron orbitals in a hydrogen atom are proportional to square unit fractions. Therefore the energy levels of photons that can be absorbed or em

From Yahoo Answers

Question:Is there a online calculator with fractions for free? Plz tell me if there iz

Answers:There are several. http://www.homeschoolmath.net/worksheets/fraction_calculator.php http://www.helpingwithmath.com/resources/cal_fractions.htm http://www.calculatorsoup.com/calculators/math/fractionssimplify.php

Question:Is there a easy to use calculator to solve fraction equations? Example: X 3X _ + 1 + __ = -9 2 4 Anything?

Answers:Is that supposed to be: (x/2) + 1 + (3x/4) = -9 The way I go about these, is to first remove the fractions by multiplying all by the LCD. In this case, it's 4. So we get: 2x + 4 + 3x = -36 Now the numbers are a little more manageable. 5x + 4 = -36 5x = -40 x = -8

Question:In 2005, 60% of drivers in the United States reported that they own a cellular phone. What fraction in lowest terms is equivalent to 60%? Could someone tell me how to do it? i know its 3/5 but how do you get that answer?

Answers:I agree with all of the above, and also want to add that there is most likely a decimal to fraction button on your calculator which comes in super-handy during a test or something when you need to do this sort of thing quickly.

Question:I have tons of math homework dealing with fractions in every sort of computation. Doing it all on paper will take me every second of non-classroom time I got, & still be incomplete. I thought windows calculator had a fraction function, but apparently it does not. Does anyone know where I can get a freeware scientific calculator that's not on trial basis, or require a credit card# to turn on? I've seen all sorts of trash but nothing useful & free. HELP!

Answers:1. Open the calculator application 2. Click on View menu 3. Select 'Scientific' menu item You are there, start using the fraction functions By default calculator runs in standard mode. You can toggle between these two modes at any time.

From Youtube

Find Equivalent Fractions :Learn to find equivalent fractions of any given fraction - brought to you by www.tenmarks.com Try it free.

Equivalent Fractions and Mixed Numbers :Learn about equivalent fractions and mixed numbers - brought to you by www.tenmarks.com Try it free.