91Ó°ÊÓ

Multiplication is a mathematical operation where you combine groups of equal sizes. For example, if you multiply 3 by 4, you are essentially adding 3, four times: \(3 + 3 + 3 + 3 = 12\). In our exercise, we multiplied -4.2 by 100. Multiplication can be applied to whole numbers, fractions, and decimals.

To multiply decimals like in this problem, treat them like whole numbers initially. Multiply the numbers without considering the decimal points: \(42 \times 100 = 4200\). Then, position the decimal point in the product: since -4.2 has one digit after the decimal, we adjust, making it 420.

Always remember to consider the signs of the numbers being multiplied, which we will explore next.

Absolute values refer to the magnitude of a number irrespective of its sign. It is always non-negative. For example, the absolute value of -4.2 is 4.2, and for 100, it is 100. This is shown by the notation \(|-4.2| = 4.2\) and \(|100| = 100\).

When you multiply two numbers, you can initially ignore their signs and work with their absolute values. In the exercise, we multiplied the absolute values: \(4.2 \times 100 = 420\). Calculating with absolute values simplifies the process, especially when signs are involved.

After obtaining the product using absolute values, you determine the final sign of the result based on the rules of multiplying positive and negative numbers.

Negative numbers are those less than zero, represented by a minus sign (-). In multiplication, the product's sign depends on the signs of the numbers being multiplied:

• If both numbers are positive, the result is positive.
• If both numbers are negative, the result is positive (negative times negative gives a positive).
• If one number is positive and the other is negative, the result is negative (positive times negative gives a negative).

In our specific exercise, we had one negative number (-4.2) and a positive number (100). Therefore, their product is negative.

Conclusively, multiplying -4.2 and 100, we first find \(4.2 \times 100 = 420\), and then apply the negative sign to conclude: \(-420\).