what is definition of unit fraction?

Answer 1

Were you aware there is a special section in Y answers for homework help? You would probably have tons of success posting your question about homework type things in the homework section.

Answer 2

Unit Fraction Definition

Answer 3

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, 1/42 etc.

The partial sum

1/1+1/2+1/3+...+1/n

gives the harmonic series, and is close to loge(n)+γ as n increases. So the sum of all unit fractions is infinite.

The product of two unit fractions is again a unit fraction; the sum and difference may be unit fractions, though are often not.

* 1/m × 1/n = 1/(mn)
o 1/2 × 1/5 = 1/10
o 1/3 × 1/6 = 1/18
* 1/m + 1/n = (n+m)/(mn)
o 1/2 + 1/5 = 7/10
o 1/3 + 1/6 = 1/2
* 1/m - 1/n = (n-m)/(mn)
o 1/2 - 1/5 = 3/10
o 1/3 - 1/6 = 1/6

Any positive rational number can be written as the sum of distinct unit fractions. The result is an Egyptian fraction, but the expression is not unique. For example

0.8 = 1/2+1/4+1/20 = 1/3+1/5+1/6+1/10.

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History

Unit fractions were used by the ancient Egyptians to facilitate mathematical computations. In modern notation Egyptian fractions may be indicated as \overline{2}, \overline{3}, \overline{4}, \overline{5} and so forth.

Unlike systems with a fixed base such as the decimal system which are forced to a long series of ever closer approximations, the variable base allowed the Egyptians to get to an exact equivalent relatively quickly.

Even irrational numbers such as π can be closely approximated using for example 3\ \overline{7} especially when using a ruler divided into parts as calculator makes the process trivially simple.

For calculations involving multiplication or division by doubling, 3\ \overline{7} may be taken as 3\ \overline{8}\ \overline{64}.

Using fractions 2/3 or 3/4 is adequate in terms of pure mathematics but breaks down in human terms as for example in distributing rations of grain and beer where the number of people is not really a variable.

Answer 4

A fraction whose numerator is 1 (eg, 1/1, 1/3, 1/x). Every nonzero number n may be written as a unit fraction, since n = 1/(1/n).

Answer 5

a fraction with one as the numerator, and a rational no. as denominator is a unit fraction

Answer 6

A fraction whose numerator is one (1)

Answer 7

the first answer itseld is enough