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Negative numbers are simply the numbers less than zero. They always have a negative sign (-) in front. Negative numbers can be your best friend once you understand them, especially when it comes to operations like multiplication and addition.
When we multiply two negative numbers, just remember this simple rule: two negatives make a positive. This means if you multiply

• -3 by -2, the result is +6.
• Similarly for our problem, -0.75 multiplied by -8 gives us a positive 6.

It's like saying removing a loss results in a gain, or taking away a negative brings positivity. A key tip is to focus on the numbers themselves, and treat the negative signs as separate entities to be considered during multiplication.
Once you’re comfortable with this concept, solving such problems becomes much easier!

Simplifying expressions is all about making calculations easier and tidier. When you simplify an expression, you condense it without changing its value.
Let's consider the expression -0.75(-8y). When simplifying:

• First, you'll want to tackle any operations, such as multiplication, between numbers.
• In our case, it's multiplying -0.75 by -8 which we discussed earlier becomes 6 due to the rules of negative numbers.

Once you've computed the numerical operation, you'll multiply this result by the variable part of your expression, which is y in this example. The final simplified expression is 6y.

Remember, simplification is about making expressions easier to handle while keeping the meaning intact.

Multiplication rules serve as a foundation for working with numbers, especially decimals and negatives. When it comes to decimals, it's important to understand:

• Multiply the numbers ignoring the decimals and signs first. So, for 0.75 and 8, just think of this as 75 times 8 which equals 600.
• Then, count the total decimal places in the numbers you are multiplying, there are two in 0.75. Finally, place the decimal in your product accordingly, resulting in 6.00 which simplifies to 6.

Now, bring in the rules for multiplying negative numbers. With two negative numbers, remember: the product is positive. Combine these two steps, and you can evaluate expressions involving negative decimals easily and accurately.
Understanding and applying these rules efficiently can turn complex problems into straightforward calculations!