The sum of unit fractions exists,
[tex]$\frac{3}{4}=\frac{1}{4}+\frac{1}{2}[/tex].
What is a unit fraction?
A unit fraction exists as a rational number written as a fraction where the numerator exists as one and the denominator exists as a positive integer. A unit fraction exists therefore the reciprocal of a positive integer, 1/n.
What is the mathematical expression of a unit fraction?
Multiplying any two unit fractions results in a product that exists another unit fraction:
[tex]$\frac{1}{x} \times \frac{1}{y}=\frac{1}{x y} .$[/tex]
However, adding, subtracting, or dividing two unit fractions has a result that exists generally not a unit fraction:
[tex]${data-answer}amp;\frac{1}{x}+\frac{1}{y}=\frac{x+y}{x y} \\[/tex]
[tex]${data-answer}amp;\frac{1}{x}-\frac{1}{y}=\frac{y-x}{x y} \\[/tex]
[tex]${data-answer}amp;\frac{1}{x} \div \frac{1}{y}=\frac{y}{x}[/tex]
Given:
3/4
To find:
the sum of unit fractions
Let,
[tex]$\frac{3}{4}=\frac{1+2}{4}[/tex]
[tex]$=\frac{1}{4}+\frac{2}{4}[/tex]
[tex]$=\frac{1}{4}+\frac{1}{2}[/tex]
[tex]$\frac{3}{4}=\frac{1}{4}+\frac{1}{2}[/tex].
Therefore, the sum of unit fractions exists,
[tex]$\frac{3}{4}=\frac{1}{4}+\frac{1}{2}[/tex].
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