Expanding a Fraction with Denominator 2 | Homework Solution

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In summary, a fraction is a mathematical expression representing a part of a whole, consisting of a numerator and denominator. To expand a fraction with a denominator of 2, both numbers must be multiplied by the same factor. This makes it easier to perform operations and compare fractions. Common methods for expanding include using the distributive property and simplifying after expansion is possible by finding the GCF of the numerator and denominator.
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Homework Statement



Expand the fraction [tex]\frac{1}{\sqrt[n]{2^5}}[/tex], for [tex]n \in \mathbb{N}[/tex] and [tex]n \geq 2[/tex], to have denominator 2.

Homework Equations

The Attempt at a Solution



[tex]\frac{1}{\sqrt[n]{2^5}} \circ \frac{\sqrt[n]{{2}^{n-5}}}{\sqrt[n]{{2}^{n-5}}}[/tex]

[tex]\frac{\sqrt[n]{{2}^{n-5}}}{2}[/tex]

Is this correct?
 
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  • #2
Looks good to me
 
  • #3
Yeah it appears ok. Odd question, though.
 

What is a fraction?

A fraction is a mathematical expression that represents a part of a whole. It consists of two numbers, the numerator and the denominator, separated by a line. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole.

How do you expand a fraction with a denominator of 2?

To expand a fraction with a denominator of 2, you need to multiply both the numerator and the denominator by the same number. This will result in an equivalent fraction with a larger denominator, making it easier to work with.

Why is it useful to expand fractions with a denominator of 2?

Expanding fractions with a denominator of 2 makes it easier to perform mathematical operations, such as addition, subtraction, multiplication, and division. It also allows for easier comparison and conversion between fractions with different denominators.

What are some common methods for expanding fractions with a denominator of 2?

There are several methods for expanding fractions with a denominator of 2. One method is to multiply both the numerator and the denominator by the same number, as mentioned before. Another method is to use the distributive property, where you multiply the numerator and denominator by a fraction that is equivalent to 1, such as 2/2 or 3/3.

Can fractions with a denominator of 2 be simplified after expanding?

Yes, fractions with a denominator of 2 can be simplified after expanding. This can be done by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF. This will result in a simplified fraction that is equivalent to the expanded fraction.

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