Find the value of 6−2 as a fraction in its simplest form.
The Correct Answer and Explanation is:
To solve for (6 – 2) and express the result as a fraction in its simplest form, we first perform the arithmetic operation:
[
6 – 2 = 4
]
Now, to express the result (4) as a fraction, we can write it as:
[
\frac{4}{1}
]
This fraction represents the integer (4) in fractional form. Now, let’s simplify this fraction. In this case, (\frac{4}{1}) is already in its simplest form because the numerator (4) and the denominator (1) have no common factors other than (1). Therefore, the simplest form of the fraction is:
[
\frac{4}{1}
]
When we discuss fractions, it is essential to understand what is meant by “simplest form.” A fraction is in its simplest form when the numerator and the denominator are relatively prime, meaning they have no common factors other than (1).
For example, if we had a fraction like (\frac{8}{12}), we could simplify it by finding the greatest common divisor (GCD) of (8) and (12), which is (4). Dividing both the numerator and the denominator by their GCD would yield (\frac{8 \div 4}{12 \div 4} = \frac{2}{3}), which is simpler.
In our case with (4), since it is expressed as (\frac{4}{1}), it signifies that there are (4) whole units (and no fractional part). Therefore, the final result, (4), expressed as a fraction in its simplest form is:
[
\frac{4}{1}
]
This illustrates both the arithmetic and the representation of the answer as a fraction, underscoring the concept of simplification and clarity in numerical representation.