What is One-Half of Two and a Half?

Understanding the concept of fractions and their operations is a fundamental part of mathematics. One such operation is finding half of a given number, which can be computed using simple arithmetic principles. Let's explore the problem of finding one-half of two and a half (2.5).

1. Direct Calculation

In this approach, we convert the mixed number 2.5 into an improper fraction.

2.5 can be written as 2 1/2, which equals 5/2. To find half of 5/2, we multiply it by 1/2.

Half of 5/2 is calculated as follows:

5/2 × 1/2 5/4

This can also be expressed as 1 1/4, which is the same as 1.25 in decimal form.

2. Multiple Interpretations

The expression "2.5 divided by 0.5" can be interpreted in two different ways:

First, as 20.5 divided by 0.5, the result is 1.5. Second, as 2.50.5, the result is 1.25.

When we directly divide 2.5 by 0.5, the calculation is clear and straightforward:

2.5 ÷ 0.5 5

Ultimately, the question asks for half of 2.5, and the arithmetic simplifies to dividing 2.5 by 2, then by 2 again:

2.5 ÷ 2 1.25

Thus, one-half of 2.5 is 1.25.

3. Alternative Interpretations Using Fraction Rules

We can also use fraction rules to solve the question. The number 2.5 can be expressed as 5/2. Using the rule that dividing by a number is the same as multiplying by its reciprocal, we can write 2.5 ÷ 2 as 5/2 × 1/2.

The multiplication of two fractions follows the rule (a/b) × (c/d) (ac)/(bd), which simplifies to:

5/2 × 1/2 5/4

This is equivalent to 1 1/4 or 1.25 in decimal form.

Finally, let's use another method involving the formula (x y/z) (xzy/z) and (a/b c/d) (ac/bd) to verify the calculation:

(2 1/2) ÷ 2 221/2 ÷ 2 5/4 1 1/4

This confirms that one-half of 2.5 is indeed 1.25, using different mathematical approaches.