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# Order of Operations with Negative Numbers

#### Grade 7 Math Worksheets

Understanding the order of operations is a crucial skill in mathematics that helps us solve complex equations and ensure consistent and accurate results.

As Grade 7 students progress in their mathematical journey, they encounter a new challenge: incorporating negative numbers into these calculations.

• Order of Operations with Negative Numbers
• Formula
• Real-life Applications
• FAQs

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## Order of Operations with Negative Numbers

The order of operations is a set of rules that guides us in solving mathematical expressions. It ensures consistency and accuracy in our calculations. Grade 7 students must grasp the concept of performing operations in a specific sequence: parentheses, exponents, multiplication and division (from left to right), and finally, addition and subtraction (from left to right).

Embracing the Negative Numbers: Negative numbers may seem intimidating, but they are an essential part of mathematics. They represent values less than zero and play a crucial role in various real-life scenarios. Understanding how to work with negative numbers allows us to solve a wider range of mathematical problems.

Tackling Parentheses and Exponents: Parentheses and exponents are the building blocks of mathematical expressions. When encountering parentheses, we should simplify the expression within them first. Exponents, on the other hand, involve raising a number to a power. Understanding their order in the overall expression is key to solving equations correctly.

Mastering Multiplication and Division: In the order of operations, multiplication and division have equal priority and are performed from left to right. When negative numbers are involved, it’s important to remember the rules for multiplying and dividing them. Knowing how to handle negative signs in these operations will help you avoid common mistakes.

Navigating Addition and Subtraction: The final step in the order of operations is addition and subtraction, also performed from left to right. With negative numbers, it’s essential to pay attention to signs and apply the appropriate rules. Adding or subtracting negative numbers can sometimes lead to unexpected results, so a solid understanding of these operations is crucial.

## Formulas

The order of operations, often remembered by the acronym PEMDAS, stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It represents the sequence in which mathematical operations should be performed within an expression.

### Adding and Subtracting Negative Numbers:

To add or subtract negative numbers, we can use the following formulas:

• Adding a negative number: a + (-b) = a – b
• Subtracting a negative number: a – (-b) = a + b

### Multiplying and Dividing Negative Numbers:

When multiplying or dividing negative numbers, the following formulas apply:

• Multiplying two negative numbers: (-a) * (-b) = ab
• Multiplying a negative and a positive number: (-a) * b = -ab
• Dividing a negative number by a positive number: (-a) / b = -(a/b)
• Dividing a positive number by a negative number: a / (-b) = -(a/b)

### Power of a Negative Number:

Raising a negative number to an even power results in a positive value, while raising it to an odd power yields a negative value.

The formula is as follows:

• Negative number raised to an even power: (-a)^n = a^n
• Negative number raised to an odd power: (-a)^n = -a^n

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## Real-life Applications

1. Finances and Banking: Managing money often involves dealing with both positive and negative values. Whether it’s calculating account balances, tracking expenses, or understanding debt and loans, knowing how to apply the order of operations with negative numbers ensures accurate financial calculations.

2. Temperature Changes: Negative numbers frequently appear when measuring temperature changes. For instance, when you see a weather forecast indicating a temperature drop of -5 degrees Celsius, understanding the order of operations allows you to determine the actual temperature after the decrease.

3. Elevations and Altitudes: In geography, negative numbers are commonly used to represent elevations and altitudes below sea level. Whether you’re studying the depth of a lake, the height of a mountain, or the altitude of an airplane, applying the order of operations helps accurately interpret and compare these values.

4. Temperature Scales: Different temperature scales, such as Celsius and Fahrenheit, often involve negative values. Converting between these scales requires correctly applying the order of operations to ensure accurate and meaningful temperature readings.

5. Physics and Mathematics: Concepts in physics and advanced mathematics frequently involve negative numbers. From analyzing vectors and directions to solving equations in calculus, understanding the order of operations with negative numbers is essential for precise calculations and problem-solving.

## FAQs

##### Why is it important to understand the order of operations with negative numbers?

Understanding the order of operations with negative numbers is crucial because it ensures accurate and consistent calculations in mathematics. By following the correct sequence of operations (parentheses, exponents, multiplication and division, and addition and subtraction), you can solve complex equations and expressions correctly. This skill is essential for various academic disciplines, real-life applications, and problem-solving scenarios.

##### How do I remember the order of operations?

A helpful mnemonic to remember the order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It provides a sequential guide for performing operations within an expression. Start by simplifying anything within parentheses or brackets, then evaluate exponents, followed by multiplication and division, and finally addition and subtraction.

##### How do I add or subtract negative numbers?

To add or subtract negative numbers, you can use the following rules:

Adding a negative number: To add a negative number, you can subtract the positive value of that number. For example, -3 + (-5) can be rewritten as -3 – 5, resulting in -8.
Subtracting a negative number: To subtract a negative number, you can change it to addition. For example, 7 – (-4) can be rewritten as 7 + 4, resulting in 11.

##### How do I multiply or divide negative numbers?

When multiplying or dividing negative numbers, the following rules apply:

Multiplying two negative numbers: When you multiply two negative numbers, the result is positive. For example, (-3) * (-4) equals 12.
Multiplying a negative and a positive number: When you multiply a negative number by a positive number, the result is negative. For example, (-3) * 4 equals -12.
Dividing a negative number by a positive number: When you divide a negative number by a positive number, the result is negative. For example, (-10) / 2 equals -5.
Dividing a positive number by a negative number: When you divide a positive number by a negative number, the result is negative. For example, 10 / (-2) equals -5.

##### How are negative numbers used in real life?

Negative numbers have numerous real-life applications. They are used to represent temperatures below zero, elevations below sea level, debts in finance, losses in accounting, temperature anomalies in weather forecasting, and direction or opposite forces in physics. Understanding how to work with negative numbers is essential in fields such as finance, science, geography, programming, and more.

##### Are negative numbers important outside of mathematics?

Yes, negative numbers have significance beyond mathematics. They are used in various fields such as finance, science, weather forecasting, programming, and even everyday situations like measuring temperatures or understanding elevations below sea level. Negative numbers allow us to describe and analyze real-world phenomena accurately and make informed decisions based on quantitative data.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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