Calculate: $7.4 - 5.89$3. Calculate: 9.64 × 10 9.64 \times 10 9.64 × 10

Introduction

Arithmetic operations are the foundation of mathematics, and mastering them is essential for success in various fields, including science, engineering, economics, and finance. In this article, we will focus on two fundamental arithmetic operations: subtraction and multiplication. We will explore the concepts, formulas, and examples of these operations, and provide step-by-step solutions to help you understand and apply them effectively.

Subtraction: A Key Arithmetic Operation

Subtraction is a fundamental arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-) and is used to calculate the result of a subtraction operation.

Formula for Subtraction

The formula for subtraction is:

a - b = c

where a is the first number, b is the second number, and c is the result of the subtraction operation.

Example 1: Calculating $7.4 - 5.89$

To calculate the result of $7.4 - 5.89$, we need to follow the order of operations (PEMDAS):

1. Subtract 5.89 from 7.4
2. The result is -1.49

Therefore, $7.4 - 5.89 = -1.49$.

Example 2: Calculating $9.64 - 3.21$

To calculate the result of $9.64 - 3.21$, we need to follow the order of operations (PEMDAS):

1. Subtract 3.21 from 9.64
2. The result is 6.43

Therefore, $9.64 - 3.21 = 6.43$.

Multiplication: A Key Arithmetic Operation

Multiplication is a fundamental arithmetic operation that involves finding the product of two numbers. It is denoted by the multiplication sign (×) and is used to calculate the result of a multiplication operation.

Formula for Multiplication

The formula for multiplication is:

a × b = c

where a is the first number, b is the second number, and c is the result of the multiplication operation.

Example 1: Calculating $9.64 \times 10$

To calculate the result of $9.64 \times 10$, we need to follow the order of operations (PEMDAS):

1. Multiply 9.64 by 10
2. The result is 96.4

Therefore, $9.64 \times 10 = 96.4$.

Example 2: Calculating $5.21 \times 3.14$

To calculate the result of $5.21 \times 3.14$, we need to follow the order of operations (PEMDAS):

1. Multiply 5.21 by 3.14
2. The result is 16.41

Therefore, $5.21 \times 3.14 = 16.41$.

Conclusion

In conclusion, mastering basic arithmetic operations such as subtraction and multiplication is essential for success in various fields. By understanding the formulas and examples provided in this article, you will be able to apply these operations effectively and solve problems with confidence. Remember to follow the order of operations (PEMDAS) and to be precise in your calculations.

Tips and Tricks

• Always follow the order of operations (PEMDAS) when performing arithmetic operations.
• Use a calculator or a computer program to check your calculations and ensure accuracy.
• Practice, practice, practice! The more you practice, the more confident you will become in applying arithmetic operations.

Common Mistakes to Avoid

• Not following the order of operations (PEMDAS) can lead to incorrect results.
• Rounding numbers incorrectly can lead to inaccurate results.
• Not checking calculations can lead to errors.

Real-World Applications

Arithmetic operations are used in various real-world applications, including:

• Finance: Calculating interest rates, investment returns, and loan payments.
• Science: Calculating distances, velocities, and accelerations.
• Engineering: Calculating stresses, strains, and loads on structures.
• Economics: Calculating GDP, inflation rates, and unemployment rates.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I calculate the result of a subtraction operation?

A: To calculate the result of a subtraction operation, follow these steps:

1. Subtract the second number from the first number.
2. The result is the difference between the two numbers.

Q: How do I calculate the result of a multiplication operation?

A: To calculate the result of a multiplication operation, follow these steps:

1. Multiply the two numbers together.
2. The result is the product of the two numbers.

Q: What is the difference between a decimal and a fraction?

A: A decimal is a way of representing a number using a point (.) to separate the whole number part from the fractional part. For example, 3.5 is a decimal.

A fraction is a way of representing a number as a ratio of two integers. For example, 3/5 is a fraction.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, follow these steps:

1. Identify the decimal.
2. Determine the place value of the last digit (e.g., tenths, hundredths, etc.).
3. Write the decimal as a fraction with the place value as the denominator.

For example, 0.5 can be written as 1/2.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, follow these steps:

1. Identify the fraction.
2. Divide the numerator by the denominator.
3. The result is the decimal equivalent of the fraction.

For example, 1/2 can be written as 0.5.

Q: What is the difference between a positive and a negative number?

A: A positive number is a number that is greater than zero. For example, 5 is a positive number.

A negative number is a number that is less than zero. For example, -5 is a negative number.

Q: How do I add and subtract positive and negative numbers?

A: When adding and subtracting positive and negative numbers, follow these rules:

• When adding two numbers with the same sign (both positive or both negative), add their absolute values and keep the same sign.
• When adding two numbers with different signs (one positive and one negative), subtract their absolute values and keep the sign of the number with the larger absolute value.
• When subtracting two numbers with the same sign, subtract their absolute values and keep the same sign.
• When subtracting two numbers with different signs, add their absolute values and keep the sign of the number with the larger absolute value.

Q: What is the difference between a whole number and a decimal?

A: A whole number is a number that is not a decimal. For example, 5 is a whole number.

A decimal is a number that has a fractional part. For example, 3.5 is a decimal.

Q: How do I round numbers to the nearest whole number?

A: To round numbers to the nearest whole number, follow these steps:

1. Identify the number.
2. Determine the place value of the last digit (e.g., tenths, hundredths, etc.).
3. If the digit in the place value is 5 or greater, round up to the next whole number.
4. If the digit in the place value is less than 5, round down to the previous whole number.

For example, 3.5 rounded to the nearest whole number is 4.

Q: What is the difference between a percentage and a decimal?

A: A percentage is a way of representing a number as a fraction of 100. For example, 25% is a percentage.

A decimal is a way of representing a number using a point (.) to separate the whole number part from the fractional part. For example, 0.25 is a decimal.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, follow these steps:

1. Identify the percentage.
2. Divide the percentage by 100.
3. The result is the decimal equivalent of the percentage.

For example, 25% can be written as 0.25.

Q: How do I convert a decimal to a percentage?

A: To convert a decimal to a percentage, follow these steps:

1. Identify the decimal.
2. Multiply the decimal by 100.
3. The result is the percentage equivalent of the decimal.

For example, 0.25 can be written as 25%.

Conclusion

In conclusion, mastering basic arithmetic operations and understanding the concepts of decimals, fractions, and percentages is essential for success in various fields. By following the order of operations (PEMDAS) and applying the rules for adding and subtracting positive and negative numbers, you will be able to solve problems with confidence and accuracy. Remember to practice, practice, practice!