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Chapter 1: Problem 50

Fill in the appropriate ordering symbol: either \(<,>,\) or \(=\). 8 + 0____4 \(\cdot\)0.

Short Answer

Expert verified
8 > 0

Step by step solution

01

Simplify the Left Side of the Equation

First, simplify the left side of the equation. Calculate the sum of 8 and 0. \[ 8 + 0 = 8 \]
02

Simplify the Right Side of the Equation

Next, simplify the right side of the equation. Multiply 4 by 0. \[ 4 \times 0 = 0 \]
03

Compare Both Sides

Now, compare the simplified results of both sides. 8 is clearly greater than 0. Therefore, we use the 'greater than' symbol (>) in the blank.

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Key Concepts

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

addition
Addition is one of the most basic operations in mathematics. It involves combining two or more numbers to get their total. In our exercise, we started with adding 8 and 0. When you add any number to zero, the result is always the number itself.

For example: \[ 8 + 0 = 8 \] This is because zero has no value and does not change the original number when added. Understanding this property of zero in addition helps simplify many math problems. Always remember that adding zero to any number leaves the number unchanged.
multiplication
Multiplication is another fundamental math operation. It's about finding the total of one number taken multiple times. For example, when you multiply 4 by 0, you are essentially taking zero groups of 4.

For example: \[ 4 \times 0 = 0 \] In any multiplication where one number is zero, the result is always zero. This is because anything multiplied by zero gives zero. This property is very useful for simplifying problems and making calculations more straightforward.
inequality symbols
Inequality symbols are used to compare two values. Common inequality symbols include '<' (less than), '>' (greater than), and '=' (equal to). In our exercise, we compared the results of two operations: \[ 8 + 0 \] and \[ 4 \times 0 \]

The result of 8 plus 0 is 8, and the result of 4 multiplied by 0 is 0. Since 8 is greater than 0, we place the 'greater than' symbol (>) between the two expressions: \[ 8 > 0 \] Understanding how to compare numbers using inequality symbols is essential for solving many math problems. It helps you determine the relationship between values, which is crucial for more advanced topics in mathematics.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$5+\\{2+4[3+3(4+2)]\\}$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$\frac{-12}{-1.2}-\frac{-10}{2.5}$$

In Exercises \(73-84\), evaluate the given expression. $$|6-2|-|2-6|$$

In Exercises \(73-84\), evaluate the given expression. $$|-4-3+2|-4-3+2$$

Sketch the given set on a number line. $$\\{x | 1 \leq x<3\\}$$
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