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:
- Changing to addition of the opposite value
- Writing addition terms as fractions over 1
- Simplifying the total fraction
This develops intuitions about arithmetic operations and connections between numbers, expressions, and fractions.
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