Problem 60 Evaluate. If an expression is un... [FREE SOLUTION]

Chapter 1: Problem 60

Evaluate. If an expression is undefined, say so. $$\frac{-14-(-2)}{-3-3}$$

Short Answer

Expert verified

$2$

Step by step solution

Simplify the Numerator

First, simplify the numerator of the expression. The numerator is $-14 - (-2)$. Subtracting a negative is the same as adding the positive, so this simplifies to $-14 + 2 = -12$.

Simplify the Denominator

Next, simplify the denominator of the expression. The denominator is $-3 - 3$. This simplifies to $-6$.

Divide the Simplified Numerator by the Simplified Denominator

Now, divide the simplified numerator by the simplified denominator:$\frac{-12}{-6}$. Dividing two negative numbers results in a positive number. Therefore, $\frac{-12}{-6} = 2$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator Simplification

To simplify a fraction, you need to simplify the numerator first. The numerator is the top part of the fraction. In our exercise, the numerator is $-14 - (-2)$.
When you have a double negative inside an expression, it becomes a positive. So, $-14 - (-2)$ becomes $-14 + 2$.
This can be easier to understand if you think of subtracting a debt: If you subtract owing $2 from owing $14, you end up owing less. So, $-14 + 2 = -12$.
Remember, when simplifying the numerator, always watch for double negatives. Changing them can simplify the problem greatly.

Denominator Simplification

Next, focus on simplifying the denominator. The denominator is the bottom part of the fraction. In the given exercise, the denominator is $-3 - 3)$.
This is straightforward since there is no double negative involved. Subtracting 3 from -3 simply means moving further to the negative side of the number line. So, $-3 - 3 = -6$.
It's important to perform these operations step by step to avoid any mistakes. Negative amounts can be tricky, but just remember to take it slowly and carefully.

Negative Number Division

Finally, let's discuss dividing negative numbers. In this exercise, we have $-12$ as the numerator and $-6$ as the denominator: $\frac{-12}{-6}$.
When you divide two negative numbers, the result is always positive. Here's why: A negative sign indicates direction. When both the numerator and denominator are negative, they cancel each other out.
So, $\frac{-12}{-6} = 2$. This rule is consistent and will always apply unless one of the numbers is positive.
This concludes why our final answer is a positive 2. Simplifying and dividing step by step helps ensure the accuracy of the result.

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91影视

Evaluate. If an expression is undefined, say so. $$\frac{-14-(-2)}{-3-3}$$

Short Answer

Step by step solution

Simplify the Numerator

Simplify the Denominator

Divide the Simplified Numerator by the Simplified Denominator

Key Concepts

Numerator Simplification

Denominator Simplification

Negative Number Division

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