Evaluate the following products without actual multiplication:

50 1/2 × 49 1/2?

To evaluate the expression 50 1/2 × 49 1/2 without performing actual multiplication, we can use a clever approach involving the difference of squares.

Understanding the Numbers

The numbers can be rewritten as:

• 50 1/2 = 50.5
• 49 1/2 = 49.5

Using the Difference of Squares

We can express the multiplication as:

(50 - 0.5)(50 - 1) = (50 - 0.5)(50 - 1) = (50 - 0.5)(50 - 1)

This can be simplified using the formula for the difference of squares:

(a - b)(a + b) = a² - b²

Identifying 'a' and 'b'

In this case:

• Let a = 50
• Let b = 0.5

Calculating the Result

Now, we can find:

50² - (0.5)² = 2500 - 0.25 = 2499.75

Thus, the value of 50 1/2 × 49 1/2 is approximately 2499.75.