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Chapter 3: Problem 74

Evaluate the given expression. $$\frac{-15-5}{-2(-5)(-2)}$$

Short Answer

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Step by step solution

01

Simplify the Numerator

Combine the terms in the numerator: \(-15 - 5 = -20\)
02

Simplify the Denominator

Multiply the terms in the denominator: \(-2 * -5 = 10\)Next, multiply by -2: \(10 * -2 = -20\)
03

Divide the Numerator by the Denominator

Now, divide the simplified numerator by the simplified denominator: \(\frac{-20}{-20} = 1\)

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Key Concepts

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

Simplifying Expressions
When solving algebraic problems, simplifying expressions is crucial.
It involves reducing expressions to their simplest form. This can mean combining like terms, which are terms that have the same variables raised to the same power.
For example, \(-15 - 5\) simplifies to \(-20\). This step makes it easier to handle larger, more complex equations. Always look for ways to reduce your expression before moving on to the next steps.
Multiplication of Integers
Multiplying integers is another essential skill in algebra. Keep in mind the rules for the sign of the product:
  • Positive 脳 Positive = Positive
  • Negative 脳 Negative = Positive
  • Positive 脳 Negative = Negative

In the given exercise, you multiply \(-2 \times -5\), which results in \(+10\). Then, multiply this product by \(-2\), to get \(-20\). Understanding these sign rules is crucial to getting the right answer in multiplication problems.
Division of Integers
Division of integers uses similar sign rules as multiplication:
  • Positive 梅 Positive = Positive
  • Negative 梅 Negative = Positive
  • Positive 梅 Negative = Negative

For the exercise, you need to divide \(-20\) by \(-20\). By following the rules, \(\frac{-20}{-20}\) equals \(+1\).
Remember to simplify both the numerator and the denominator before dividing, as it simplifies the task and reduces the chance of errors.

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