91Ó°ÊÓ

Absolute values are the non-negative values of any given number, regardless of its sign. The absolute value of a number is its distance from 0 on a number line. So, whether a number is positive or negative, its absolute value is always positive.
For instance:
\begin{itemize} \begin{item} The absolute value of -7 is 7 (denoted as \(|-7| = 7\)). ewline \begin{item} The absolute value of 5 is 5 (denoted as \(|5| = 5\)). ewline ewline In the given example, to multiply -10 and -17.5, we first consider their absolute values.ewline The absolute value of -10 is 10, and the absolute value of -17.5 is 17.5. Next, we need to multiply these absolute values.

Multiplication is one of the basic arithmetic operations and can be thought of as repeated addition. When you multiply two numbers, you're essentially adding one number to itself repeatedly. ewline In the context of our problem, we need to multiply the absolute values of -10 and -17.5 which translates to multiplying 10 and 17.5. ewline To do this, use the standard multiplication method: ewline \(10 \times 17.5 = 175\). ewline Multiplication also involves rules for dealing with positive and negative numbers:
\begin{ul}\begin{item} A positive number multiplied by a positive number results in a positive number.ewline \begin{item} A negative number multiplied by a negative number results in a positive number.ewline \begin{item} A positive number multiplied by a negative number results in a negative number.ewline ewline In our problem, both numbers are negative, and according to the rules, the product of two negative numbers is positive.

When dealing with multiplication of negative numbers, it's important to remember that the product of two negative numbers is always positive. This can be understood through the concept of absolute values which we discussed earlier. By converting the negative numbers to their absolute values and multiplying them, the result obtained is positive by nature of definition.
For our example, multiplying -10 and -17.5 results in:
\((10) \times (17.5) = 175 \). ewlineIn conclusion, multipliing the absolute values of -10 and -17.5, we get 175, which is a positive result. Understanding these basic rules helps in confidently approaching such multiplication problems in future.