Which Expression Represents 60 Divided By The Product Of 4 And 3?Choose One Answer:A. { (60 \div 4) \times 3$}$B. { (4 \times 3) \div 60$}$C. ${ 60 \div (4 \times 3)\$}
Introduction
Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is a language that helps us describe the world around us, from the simplest arithmetic operations to the most complex mathematical theories. In this article, we will delve into the world of mathematical expressions, focusing on the concept of division and multiplication. We will explore the different ways to represent mathematical operations and evaluate algebraic statements.
Division and Multiplication: A Brief Overview
Division and multiplication are two fundamental arithmetic operations that are used to solve mathematical problems. Division is the process of sharing a certain number of items into equal groups, while multiplication is the process of adding a certain number a specified number of times. In mathematical expressions, division is represented by the symbol / or ÷, while multiplication is represented by the symbol ×.
Evaluating Algebraic Statements
Algebraic statements are mathematical expressions that contain variables, constants, and mathematical operations. To evaluate an algebraic statement, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
The Problem: 60 Divided by the Product of 4 and 3
The problem we are trying to solve is: Which expression represents 60 divided by the product of 4 and 3? To solve this problem, we need to follow the order of operations and evaluate the expressions given in the options.
Option A: (60 ÷ 4) × 3
Option A represents the expression (60 ÷ 4) × 3. To evaluate this expression, we need to follow the order of operations. First, we need to divide 60 by 4, which gives us 15. Then, we need to multiply 15 by 3, which gives us 45.
Option B: (4 × 3) ÷ 60
Option B represents the expression (4 × 3) ÷ 60. To evaluate this expression, we need to follow the order of operations. First, we need to multiply 4 by 3, which gives us 12. Then, we need to divide 12 by 60, which gives us 0.2.
Option C: 60 ÷ (4 × 3)
Option C represents the expression 60 ÷ (4 × 3). To evaluate this expression, we need to follow the order of operations. First, we need to multiply 4 by 3, which gives us 12. Then, we need to divide 60 by 12, which gives us 5.
Conclusion
In conclusion, the correct expression that represents 60 divided by the product of 4 and 3 is Option C: 60 ÷ (4 × 3). This expression follows the order of operations and evaluates to 5.
Understanding the Order of Operations
The order of operations is a fundamental concept in mathematics that helps us evaluate algebraic statements. By following the order of operations, we can ensure that mathematical expressions are evaluated correctly and consistently.
Common Mistakes to Avoid
When evaluating algebraic statements, there are several common mistakes to avoid. These include:
- Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
- Not evaluating expressions inside parentheses first: Failing to evaluate expressions inside parentheses first can lead to incorrect results.
- Not multiplying and dividing from left to right: Failing to multiply and divide from left to right can lead to incorrect results.
Real-World Applications
The concept of division and multiplication has numerous real-world applications. These include:
- Cooking: When cooking, we often need to divide ingredients into equal portions. For example, when making a cake, we may need to divide 2 cups of flour into 4 equal portions.
- Shopping: When shopping, we often need to multiply prices by the number of items we are purchasing. For example, when buying 3 shirts at $20 each, we need to multiply $20 by 3 to get the total cost.
- Science: In science, we often need to divide and multiply quantities to solve problems. For example, when calculating the area of a rectangle, we need to multiply the length by the width.
Conclusion
Q: What is the difference between division and multiplication?
A: Division and multiplication are two fundamental arithmetic operations that are used to solve mathematical problems. Division is the process of sharing a certain number of items into equal groups, while multiplication is the process of adding a certain number a specified number of times.
Q: How do I evaluate an algebraic statement that contains division and multiplication?
A: To evaluate an algebraic statement that contains division and multiplication, you need to follow the order of operations (PEMDAS). This means that you need to evaluate expressions inside parentheses first, then multiply and divide from left to right, and finally add and subtract from left to right.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a mnemonic device that helps you remember the order in which to evaluate mathematical expressions. PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an expression that contains multiple operations?
A: To evaluate an expression that contains multiple operations, you need to follow the order of operations (PEMDAS). This means that you need to evaluate expressions inside parentheses first, then multiply and divide from left to right, and finally add and subtract from left to right.
Q: What is the difference between a fraction and a decimal?
A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. For example, the fraction 1/2 represents one half of a whole. A decimal is a way of expressing a fraction as a number with a point (.) separating the whole number part from the fractional part. For example, the decimal 0.5 represents one half of a whole.
Q: How do I convert a fraction to a decimal?
A: To convert a fraction to a decimal, you need to divide the numerator (the top number) by the denominator (the bottom number). For example, to convert the fraction 1/2 to a decimal, you need to divide 1 by 2, which gives you 0.5.
Q: How do I convert a decimal to a fraction?
A: To convert a decimal to a fraction, you need to express the decimal as a ratio of two numbers. For example, to convert the decimal 0.5 to a fraction, you need to express it as 1/2.
Q: What is the difference between a percentage and a decimal?
A: A percentage is a way of expressing a part of a whole as a ratio of 100. For example, the percentage 25% represents one quarter of a whole. A decimal is a way of expressing a fraction as a number with a point (.) separating the whole number part from the fractional part. For example, the decimal 0.25 represents one quarter of a whole.
Q: How do I convert a percentage to a decimal?
A: To convert a percentage to a decimal, you need to divide the percentage by 100. For example, to convert the percentage 25% to a decimal, you need to divide 25 by 100, which gives you 0.25.
Q: How do I convert a decimal to a percentage?
A: To convert a decimal to a percentage, you need to multiply the decimal by 100. For example, to convert the decimal 0.25 to a percentage, you need to multiply 0.25 by 100, which gives you 25%.
Conclusion
In conclusion, the concepts of division and multiplication are fundamental aspects of mathematics that have numerous real-world applications. By understanding the order of operations and evaluating algebraic statements correctly, we can ensure that mathematical expressions are evaluated consistently and accurately.