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In the fascinating world of mathematics, we encounter a diverse range of concepts that expand our understanding of numbers and their operations. Among these, the realm of negative numbers stands out as a perplexing yet captivating domain.

As we venture into Grade 7, we embark on a journey to unravel the mysteries of negative number addition. This crucial skill not only equips us with the ability to solve real-life problems but also serves as a stepping stone for more advanced mathematical concepts.

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Before we jump into adding negative numbers, let’s make sure we understand what they represent. Negative numbers are a way to describe quantities less than zero.

They have a “-” sign in front of them and can be thought of as numbers that move us in the opposite direction on the number line.

We’ll explore how negative numbers come into play in real-life situations.

The Rules of Negative Number Addition: Adding negative numbers involves a few key rules that help us determine the sign of the sum. We’ll learn about the “minus plus minus” rule and the “minus plus plus” rule, which guide us when adding different combinations of positive and negative numbers. These rules will enable us to perform accurate calculations and make sense of the results.

Applying Negative Number Addition: Now that we understand the rules, it’s time to put them into practice! We’ll tackle various examples and word problems that involve adding negative numbers. From temperature changes to financial transactions, negative number addition plays a crucial role in solving real-world scenarios. We’ll sharpen our problem-solving skills by applying the concepts we’ve learned.

Building Confidence and Fluency: Working with negative numbers may initially feel challenging, but with practice, it becomes easier and more intuitive. We’ll engage in interactive exercises and activities to reinforce our understanding of negative number addition. Through repetition and application, we’ll build confidence in handling these calculations efficiently.

## Rules To add two negative numbers together, simply ignore the negative signs and add the numbers as if they were positive. The result will have a negative sign. For example:

-5 + (-3) = -8

Adding a Negative Number and a Positive Number:

When adding a negative number and a positive number, subtract the absolute value of the negative number from the positive number. The sign of the result will be the same as the number with the greater absolute value. For example:

4 + (-7) = -3

When adding multiple negative numbers, you can add them in any order. The sum will be negative, and the order of the numbers will not affect the result. For example:

-2 + (-4) + (-6) = -12

Adding a Negative Number and Zero:

When adding a negative number and zero, the sum will be the negative number itself. For example:

-9 + 0 = -9

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## Real-life Examples

Example 1: Temperature Changes

Suppose the temperature at noon is 5 degrees Celsius, and it drops by 8 degrees Celsius in the afternoon. To find the new temperature, we can add the change in temperature (-8 degrees) to the initial temperature:

5 + (-8) = -3

The new temperature is -3 degrees Celsius, indicating a decrease in temperature.

Example 2: Financial Transactions

Imagine you have \$50 in your bank account, but you spend \$75 on shopping. To determine your new account balance, we can add the negative amount spent (-75 dollars) to your initial balance:

50 + (-75) = -25

Your new account balance is -\$25, indicating a deficit or negative balance.

Example 3: Elevation Changes

Suppose you start hiking at an elevation of 500 meters above sea level, and you descend 350 meters into a valley. To find your new elevation, we can add the change in elevation (-350 meters) to the initial elevation:

500 + (-350) = 150

Your new elevation is 150 meters above sea level, indicating a descent from the starting point.

Example 4: Football Yardage

In a football game, a team loses 10 yards due to a penalty. If they were originally at the 50-yard line, we can calculate their new position by adding the negative yardage (-10 yards) to the starting position:

50 + (-10) = 40

Their new position is at the 40-yard line, indicating a setback.

Example 5: Debts and Credits

Consider a scenario where you owe \$200 to a friend, but they owe you \$150. To determine the net amount owed, we can add the negative debt (-\$200) and the positive credit (+\$150):

-200 + 150 = -50

The net amount owed is -\$50, indicating that you still owe your friend \$50.

Learning about negative number addition is essential because it helps us understand and solve real-life problems involving quantities that are less than zero. It expands our mathematical skills, enhances problem-solving abilities, and forms the foundation for more advanced mathematical concepts.

##### What happens when we add two negative numbers together?

When adding two negative numbers, you can ignore the negative signs and add the numbers as if they were positive. The sum will have a negative sign. For example, -5 + (-3) = -8.

##### How do I add a negative number and a positive number?

To add a negative number and a positive number, subtract the absolute value of the negative number from the positive number. The sign of the result will be the same as the number with the greater absolute value. For example, 4 + (-7) = -3.

##### Can you add multiple negative numbers together?

Yes, you can add multiple negative numbers together. The order in which you add them does not affect the result. The sum will be negative, regardless of the order in which the numbers are added. For example, -2 + (-4) + (-6) = -12.

##### How does negative number addition relate to real-life situations?

Negative number addition is relevant in various real-life situations. It can be applied to temperature changes, financial transactions, elevation changes, sports statistics, and many other scenarios where quantities can decrease or go below zero. Understanding negative number addition helps us solve problems accurately and interpret the results in practical contexts.

##### How can I practice and improve my skills in negative number addition?

Practice is key to improving your skills in negative number addition. Work on solving a variety of problems and exercises that involve adding negative numbers. You can find practice problems in textbooks, online resources, or ask your teacher for additional practice materials. The more you practice, the more confident and fluent you’ll become in adding negative numbers. 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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