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Chapter 1: Problem 49

Fill in the appropriate ordering symbol: either \(<,>,\) or \(=\). 8 - 8_____4 \(\cdot\) 0.

Short Answer

Expert verified
0 = 0

Step by step solution

01

Solve the Left Side of the Equation

Calculate the value of the left side, which is given by the expression: \(8 - 8\). This simplifies to \(0\).
02

Solve the Right Side of the Equation

Calculate the value of the right side, which is given by the expression: \(4 \cdot 0\). This simplifies to \(0\).
03

Compare Both Sides

Compare the values on both sides. The left side is \(0\) and the right side is also \(0\). Therefore, \(0 = 0\).

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Key Concepts

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

Order of Operations
When solving math problems, it's essential to follow the correct order of operations to avoid mistakes. The standard order of operations is remembered by the acronym PEMDAS:
  • P: Parentheses first
  • E: Exponents (i.e., powers and roots, etc.)
  • MD: Multiplication and Division (left-to-right)
  • AS: Addition and Subtraction (left-to-right)
Always perform operations inside parentheses first, then handle exponents. Next, move from left to right, performing all multiplication and division. Finally, complete addition and subtraction from left to right. In the exercise you studied, the operations on each side (subtraction and multiplication) were straightforward but still needed to be properly ordered to get to the right comparison.
Basic Arithmetic
Basic arithmetic forms the foundation of math. It includes the operations of addition, subtraction, multiplication, and division. For example, in the problem given:
  • The left side, 8 - 8, involves subtraction. Subtraction means finding the difference between numbers. Here, subtracting 8 from 8 results in 0.
  • The right side, 4 × 0, involves multiplication. Multiplication is repeated addition. Whenever you multiply any number by 0, the result is 0.
Understanding these basic operations is crucial for solving more complex math problems. Knowing definitions and how to apply each operation correctly helps you achieve accurate results.
Equivalent Expressions
An essential concept in algebra is recognizing equivalent expressions. These are different expressions that evaluate to the same value. The exercise you worked through illustrated this:
  • The expression on the left side, 8 - 8, simplifies to 0.
  • The expression on the right side, 4 × 0, also simplifies to 0.
Since both sides simplify to the same value, they are equivalent. Therefore, using the equality symbol (=) is appropriate. Identifying equivalent expressions helps in simplifying algebraic expressions and solving equations efficiently.

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Most popular questions from this chapter

Factor the given number into its prime factors. If the number is prime, say so. $$1,904$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$-2(-5.3)$$

Evaluate the given expression. Remember to follow the order of operations. $$15+12 \div 6-3$$

In Exercises \(73-84\), evaluate the given expression. $$9-5 \cdot 4-2$$

In Exercises \(1-72\), compute the value of each expression. $$-561-412-(-678)$$
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