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Chapter 8: Problem 69

Perform the indicated operations. $$45 \times \frac{9}{1}$$

Short Answer

Expert verified
The result of the operation is 405.

Step by step solution

01

Understand the Problem

The exercise asks us to multiply 45 by the fraction \( \frac{9}{1} \). To do this, we need to remember that \( \frac{9}{1} \) is equivalent to 9 because any number divided by 1 is the number itself.
02

Perform the Multiplication

Multiply 45 by 9. This can be calculated as follows:\[45 \times 9 = 405\] Thus, the result of the operation is 405.

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Key Concepts

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

Understanding Fractions
Fractions represent parts of a whole and consist of two numbers separated by a slash. The top number is the numerator, and the bottom is the denominator. In the fraction \( \frac{9}{1} \), the numerator is 9 and the denominator is 1. Any number divided by 1 remains unchanged, highlighting a key property of fractions: dividing by one yields the original numerator. So, in our example, \( \frac{9}{1} = 9 \). This makes fractions versatile tools in arithmetic operations, allowing them to seamlessly convert between fractional and whole number forms.
A Step-by-Step Solution Approach
Solving math problems step by step helps structure your approach, ensuring each part of the problem is tackled methodically. Here's how you can approach a multiplication problem like \( 45 \times \frac{9}{1} \):
  • Identify and Understand: Know what the fractions represent. Here, \( \frac{9}{1} \) simplifies to 9.
  • Set Up the Operation: Recognize the multiplication of a whole number by a fraction, simplifying if needed beforehand.
  • Perform the Calculation: Multiply 45 by 9 to get to the solution.
  • Verify Your Result: Always check your work. Multiply again if needed, to confirm the correctness of your answer.
This structured method not only aids in reaching the correct answer but also builds confidence in tackling more complex problems.
Introduction to Prealgebra
Prealgebra lays the groundwork for understanding basic number operations involving whole numbers, fractions, and simple mathematical expressions. It's all about familiarizing yourself with operations such as addition, subtraction, multiplication, and division. In particular, understanding how numbers relate to one another through these operations is key. Multiplying numbers like in the exercise \( 45 \times \frac{9}{1} \) introduces you to fundamental concepts and operations necessary for algebraic thinking. As you become comfortable with these basics, advancing into algebra becomes a seamless transition.
Exploring Number Operations
Number operations such as addition, subtraction, multiplication, and division form the core of arithmetic. When multiplying numbers, like 45 and the fraction \( \frac{9}{1} \), the operation involves stretching or scaling one number by another. Here鈥檚 what you need to keep in mind with multiplication:
  • Commutative Property: The order doesn鈥檛 matter. \( a \times b = b \times a \).
  • Associative Property: Grouping doesn鈥檛 change the outcome. \( (a \times b) \times c = a \times (b \times c) \).
  • Identity Element: Any number multiplied by 1 remains unchanged.
Understanding these properties ensures a robust grasp of how different operations work together to manipulate and transform numbers.

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Most popular questions from this chapter

Set up the following problems as you have been doing. Then use a calculator to perform the actual calculations. Round answers to two decimal places where appropriate. The Badlands National Monument in South Dakota was established in \(1929 .\) It covers \(243,302\) acres of land. What is the area in square miles?

Perform the indicated operations. $$36 \times \frac{9}{1}$$

Set up the following conversions as you have been doing. Then perform the calculations on a calculator. The tip of the TV tower at the top of the Empire State Building in New York City is \(1,472\) feet above the ground. Express this height in miles to the nearest hundredth.

Write your answers as whole numbers, proper fractions, or mixed numbers. Find each product. (Multiply) $$\frac{7}{9} \cdot \frac{3}{14}$$

Perform the indicated operations. $$75 \times 43,560$$
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