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Chapter 1: Problem 70

Perform each indicated operation. $$ \frac{-12(-5)}{7-(-5)} $$

Short Answer

Expert verified
5

Step by step solution

01

- Simplify the Numerator

Evaluate the expression in the numerator: \(-12 \times -5\). Multiplying two negative numbers gives a positive product. So, \(-12 \times -5 = 60\).
02

- Simplify the Denominator

Evaluate the expression in the denominator: \(7 - (-5)\). Subtracting a negative number is the same as adding the positive counterpart. Therefore, \(7 - (-5) = 7 + 5 = 12\).
03

- Divide the Results

Divide the simplified numerator by the simplified denominator: \(\frac{60}{12}\). Simplifying this fraction gives us \(60 \, \div \; 12 = 5\).

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Key Concepts

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

Numerator Simplification
Numerator simplification is the first step when working with fractions. In this exercise, the numerator is \(-12 \times -5\). To simplify it, we need to multiply these two numbers. Remember, when you multiply two negative numbers, the result is a positive number. So, \(-12 \times -5 = 60\). This means the simplified numerator is 60. Simplifying the numerator makes the fraction easier to work with in the next steps.
Denominator Simplification
The second step in fraction operations is simplifying the denominator. Here, the denominator is \(7 - (-5)\). Subtracting a negative number is equivalent to adding its positive counterpart. So, \(7 - (-5) = 7 + 5 = 12\). This means the simplified denominator is 12. Like the numerator, a simplified denominator makes the fraction easier to handle during division.
Dividing Fractions
The final step is dividing the simplified numerator by the simplified denominator. For our given problem, the fraction we have now is \(\frac{60}{12}\). To find the result, we simply divide 60 by 12 which equals 5. So, the fraction \(\frac{60}{12}\) simplifies to 5. Make sure to perform division carefully and check your work. Dividing correctly ensures you get the right answer.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. When 6 is added to a number, the result is \(-3\)

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