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Chapter 1: Problem 62

Evaluate each of the following expressions, if possible. $$\frac{10(2)(-4)}{10(2)-4}$$

Short Answer

Expert verified
-5

Step by step solution

01

Evaluate the numerator

The numerator is given as \(10(2)(-4)\). Multiply these values together:\[10 \times 2 \times (-4) = 20 \times (-4) = -80\]
02

Evaluate the denominator

The denominator is given as \(10(2)-4\). First, perform the multiplication inside the parentheses:\[10 \times 2 = 20\]Then, subtract 4:\[20 - 4 = 16\]
03

Divide the evaluated numerator by the evaluated denominator

Now, divide the result of the numerator by the result of the denominator:\[-80 \text{ divided by } 16 = -5\]

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Key Concepts

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

Numerator and Denominator
In algebra, fractions consist of two main parts: the numerator and the denominator. The numerator is the top part of the fraction, and the denominator is the bottom part. Both parts play essential roles in solving algebraic expressions. For instance, in the given exercise, the numerator is \[10(2)(-4)\] and the denominator is \[10(2)-4\]. The numerator and denominator need to be simplified separately before solving the overall fraction.
  • Numerator: The value at the top of the fraction
  • Denominator: The value at the bottom of the fraction
By properly evaluating each part, you ensure an accurate result for the entire expression.
Multiplication and Division
In algebra, multiplication and division are key operations. Let's break down how to perform these correctly using the given example.For multiplication, follow this process: Start by multiplying the numbers in the numerator, \[10(2)(-4)\]. First, do the multiplication step by step:
  • Multiply 10 and 2, getting 20
  • Then multiply 20 by -4, getting -80
Division is the process of determining how many times one number is contained within another. In this exercise, after finding the numerator as -80 and the denominator as 16, you divide -80 by 16:
  • Perform the division: \[-80 \text{ divided by } 16 = -5\]
These steps illustrate how each operation needs careful execution to solve the algebraic expression correctly.
Steps in Solving Algebraic Problems
To solve algebraic expressions efficiently, follow a simple step-by-step approach. The given exercise serves as a good example of this method.
  1. Evaluate the Numerator: First, determine the value of the numerator by performing any necessary operations. In the example, you have \[10(2)(-4)\] which simplifies to -80.
  2. Evaluate the Denominator: Next, simplify the denominator. For the given problem, \[10(2)-4\] results in 16.
  3. Divide: Finally, divide the evaluated numerator by the evaluated denominator. With a numerator of -80 and a denominator of 16, the final answer is -5.
Following these clear and structured steps helps avoid errors and ensures you understand each stage of the problem.

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Most popular questions from this chapter

In Exercises \(73-84\), evaluate the given expression. $$|7-10|-(7-10)$$

Graph the given set on a number line. \(\\{x | x \text { is an even natural number less than } 10\\}\)

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