A detailed explanation aimed at 45-year-olds on how to simplify decimals and the significance of additional terms in equations.
Let's break down your question step by step to clarify any confusion regarding the simplification of the decimal 0.66 and the relevance of subtracting -6.
1. **Simplifying 0.66**: You started correctly by expressing 0.66 as a fraction. The decimal 0.66 can be written as:
0.66 = 66/100
Next, you simplify this fraction. Both the numerator (66) and the denominator (100) can be divided by 2:
66 ÷ 2 = 33 and 100 ÷ 2 = 50
Thus, 0.66 simplifies to:
0.66 = 33/50
2. **Understanding -6**: Now, regarding the addition of -6 (or subtracting it, as it seems you might be referencing a negative value). To determine whether -6 is just a point of clarification or a necessary part of the calculation, we need to see its context:
-6 could represent part of an equation where you are required to maintain the integrity of the original mathematical intention. For instance, if you were solving an equation like:
x + 0.66 = -6
In this case, you need to isolate x, which means you will subtract 0.66 from both sides, leading to:
x = -6 - 0.66
3. **Subtracting -6**: Therefore, subtracting -6 from the equation serves a specific purpose—it helps you find the value of x. It’s not merely to prove a point but rather a necessary operation to maintain the validity of the equation.
4. **Conclusion**: In summary, simplifying from 0.66 to 33/50 is a critical first step in handling fractions, while handling terms like -6 is crucial in ensuring that you solve equations accurately. Always consider the structure of the equation you're working with and each term's purpose to fully understand the representation.