compound fractions

what is the fraction ?
the fraction is dividing the numerator by the denominator for example

but a compound fraction is a fraction where the numerator or denominator or both are fractions , for example

now we want to find the product of 
 


we say three contain 6 halves so that

then the rule of the compound fractions is

Albert Einstein

Albert Einstein was born in the German city of Ulm on March 14, 1879 and spent age Ivaath in Munich.His father was a "Hermann Einstein" works in the sale of feathers used in the manufacture of pillows, and his mother worked "Ni Pauline hut" with him in the management of a small workshop to manufacture electrical appliances after giving up the profession of selling feathers. Delayed Einstein child in pronunciation even three years old, but he showed a passion for great nature, and the ability to understand mathematical concepts difficult, has been studied alone Euclidean geometry, and in spite of his membership in the Jewish, the income of Einstein's middle school a Catholic and received lessons in playing the violin, but Einstein rejected the idea of ​​personal god and religions are full and his private letters show that he believed in Spinoza's God is nature. In five years old his father gave him a compass, and Einstein realized then that there is strength in space are influencing the compass needle and you move. He was suffering from difficulty in comprehension, and was probably due to the shyness in childhood. Rumour has it that Einstein's child had failed the math later, however, likely that the amendment in the evaluation of grades students then raised that the child had been delayed and Einstein failed in mathematics. And the adoption of two of uncles Einstein's care and attention that child support science in general Vzodah books related to science and mathematics. After repeated losses of the workshop set up by his parents in 1894, his family moved to the city of Pavia in Italy, took advantage of Einstein's son the opportunity to withdraw from school in Munich, which dislike the strict regime stifling, and spirit. And he spent Einstein years old with his parents in the city of Milan in order to show that he must determine the way in life shuddered to his high school in the town of Arua, Switzerland, and progress after the exams the Swiss Federal Institute of Technology in Zurich in 1895, was like Einstein's methods of teaching it, and was often Maigtta of his time to study physics alone, or playing the violin, that passed the examinations and graduated in 1900, but the teachers did not choose him to enter the university.

why any number to the zero power except zero gives 1

you know that when dividing numbers with the same base , raised to the powers , we subtract the power of the divisor from that of the dividend .

now

and we know that any number divisible by zero has no meaning
finally
any number to the zero power except zero gives  1

The Least Common Denominator

our goals to add or subtract two fractions having the same denominator . now we could compute

and

while 18 is a common denominator in the above example and 6 is the smallest common denominator

adding and subtracting fractions with unlike denominators

if we need to find the sum or difference of two fractions having different denominators , then we must rewrite one or both fractions so that they have the same denominator
for example
now we find the sum

it is difficult to add
then we use equality of two fractions

now we add three twelfths and four twelfths and the product equal seven twelfths

finally

adding and subtracting fractions with like denominators

if we want to add or subtract two fractions having the same denominators we only need to add or subtract their numerators . the rule is

and

for example 
now we examine the sum of one third and two thirds . we adding one third to two thirds give us a total of three thirds which agree with  the formula

the Greatest Common Divisor

The Greatest Common Divisor
Fortunately there is a less tedious method for writing a fraction in its lowest
terms. We find the largest number that divides both the numerator and the
denominator. This number is called the greatest common divisor (GCD). We
factor the GCD from the numerator and denominator and then we rewrite
the fraction in the form: