91Ó°ÊÓ

When multiplying fractions, the operation is straightforward. You simply need to multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
For example, if you multiply \(\frac{a}{b} \times \frac{c}{d}\), you get \(\frac{a \times c}{b \times d}\).
In our exercise, we are multiplying \(\frac{1}{2}\) by -684. Since -684 can be expressed as \(\frac{-684}{1}\), our multiplication becomes \(\frac{1}{2} \times \frac{-684}{1}\). Following our rule, the result is \(\frac{1 \times -684}{2 \times 1} = \frac{-684}{2} = -342\). Understanding this method helps when dealing with more complex fraction multiplications.
Always remember to simplify the result, if possible, for ease of understanding.

Negative integers are numbers less than zero and are often represented with a minus sign (-). Handling negative numbers in multiplication follows specific rules.
If you multiply a positive number by a negative number, the result will always be negative. For instance, in our exercise, we multiply \(\frac{1}{2}\) by -684.
Since \(\frac{1}{2}\) is positive and -684 is negative, their product is negative: \(\frac{1}{2} \times -684 = -342\).
Conversely, when you multiply two negative numbers, the product will be positive. Understanding these rules helps a lot in simplifying arithmetic problems involving negative integers.

Basic arithmetic operations include addition, subtraction, multiplication, and division. Each operation follows specific rules and properties. Here, we'll focus on multiplication since our exercise involves it.
In multiplication:

• The product of two numbers is obtained by adding one of the numbers to itself a certain number of times defined by the other number.
• This operation is associative, meaning \((a \times b) \times c = a \times (b \times c)\).
• It's also commutative: \((a \times b = b \times a)\).

In our exercise, we multiply a fraction by an integer. To do this, you first express the integer as a fraction: \(\frac{1}{2} \times \frac{-684}{1}\), follow the rules of multiplying fractions, and simplify: \(\frac{1 \times -684}{2 \times 1} = \frac{-684}{2} = -342\).
Mastering these basic operations is crucial for understanding more complex math concepts.