1/2 as a Fraction?

1/2 as a Fraction?

1/2 as a fraction is already in its simplest form. It cannot be further reduced because the numerator (1) and the denominator (2) do not share a common factor other than 1. Therefore, 1/2 is the simplest fraction representation for the value one-half.

Understanding Negative Number Subtraction

In arithmetic and algebra, we encounter operations like subtracting a negative number such as 1-2. While we can calculate the value as 3, it is useful to understand how to represent the expression as a fraction to build foundational knowledge.

Let’s look at rewriting 1-2 in fractional form:

Modeling Subtraction

Subtraction can be modeled as the difference between two values on the number line:

1 – 2

Means start at 1, then move 2 units to the left. This results in landing on 3.

So 1 – 2 = 3

Representing as a Fraction

To write this as a fraction:

1 – 2 = 1 + -2

The subtraction sign is replaced with addition of the opposite value -2.

Then the expression is fractioned:

1 + -2 ——-
1

The 1 on bottom represents the starting point.

This gives us the fractional form:

1 — 1

-2 —- 1

Simplifying the Fraction

Combining the fractions gives:

1 – 2 = 3/1 = 3

The numerical result is the same. But the fractional representation builds algebraic understanding.

In summary, subtracting a negative number can be re-expressed by:

1. Changing to addition of the opposite value
2. Writing addition terms as fractions over 1
3. Simplifying the total fraction

This develops intuitions about arithmetic operations and connections between numbers, expressions, and fractions.