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# Word Problems On Negative Number Addition And Subtraction

Understanding how to add and subtract negative numbers is a fundamental skill in mathematics. While it may seem daunting at first, with practice and a clear understanding of the rules, you’ll find that it’s not as complex as it appears.

Let’s explore the basics of adding and subtracting negative numbers

When you’re adding two negative numbers, you’re essentially combining values that are below zero. The sum of two negative numbers is negative, and the absolute value of the sum is the sum of the absolute values of the numbers.

For example

(-3) + (-4) = -7

(-6) + (-2) = -8

(-10) + (-7) = -17

In each case, adding two negative numbers results in a negative sum.

When adding a positive and a negative number, you’re essentially finding the difference between the two values. Subtract the smaller number’s absolute value from the larger number’s absolute value and use the larger number’s sign for the result.

For example

(-5) + 3 = -2

(-8) + 6 = -2

(-10) + 8 = -2

In each case, adding a positive and a negative number results in a negative sum.

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## Subtraction of Negative Numbers

Subtraction of negative numbers can be approached as addition. When you subtract a negative number, it’s equivalent to adding its absolute value.

For example

5 – (-3) = 5 + 3 = 8

8 – (-2) = 8 + 2 = 10

10 – (-7) = 10 + 7 = 17

In each case, subtracting a negative number is equivalent to adding a positive number.

### Different Sign Subtraction

When subtracting a positive number from a negative number, treat it as adding the negative of that positive number.

For example

(-5) – 3 = (-5) + (-3) = -8

(-8) – 6 = (-8) + (-6) = -14

(-10) – 8 = (-10) + (-8) = -18

In each case, subtracting a positive number from a negative number results in a negative difference.

Tips for Mastering Negative Number Addition and Subtraction:

• Remember the basic rule: “Same sign, add and keep, different sign, subtract and take the sign of the bigger number.”
• Practice regularly with a variety of examples to reinforce understanding.
• Visualize number line representations to grasp concepts more intuitively.
• Break down complex problems into simpler steps.
• Seek help from teachers, peers, or online resources if you encounter difficulties.

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## Word Problems involving Negative Number Addition and Subtraction

### 1. Temperature Changes

The temperature in a city drops by 8 degrees Celsius overnight. If the current temperature is -3 degrees Celsius, what will the temperature be tomorrow morning?

Solution

-3 (current temperature) – 8 (drop in temperature) = -11

The temperature tomorrow morning will be -11 degrees Celsius.

### 2. Debt Reduction

Sarah owes \$50 to her friend, and she pays back \$20. What is her remaining debt?

Solution

\$50 (initial debt) – \$20 (payment) = \$30

Sarah’s remaining debt is \$30.

### 3. Elevator Descent

An elevator descends 6 floors from ground level. If the starting floor is -3, which floor does the elevator reach?

Solution

-3 (starting floor) – 6 (descended floors) = -9

The elevator reaches the -9th floor.

### 4. Bank Account Transactions

John’s bank account has a balance of -\$80. If he deposits \$50 and then withdraws \$30, what is his final balance?

Solution

-\$80 (initial balance) + \$50 (deposit) – \$30 (withdrawal) = -\$60

John’s final balance is -\$60.

### 5. Football Yardage

A football team loses 15 yards due to a penalty. If they were initially at -5 yards, where do they end up on the field?

Solution

-5 (initial yardage) – 15 (penalty) = -20

The football team ends up at the -20-yard line.

### 6. Weight Loss

Maria weighs 150 pounds and loses 8 pounds. What is her new weight?

Solution

150 (initial weight) – 8 (weight loss) = 142

Maria’s new weight is 142 pounds.

### 7. Scuba Diving Depth

A scuba diver descends 25 meters underwater. If the surface is considered 0 meters, how deep is the diver?

Solution

0 (surface level) – 25 (descent) = -25

The diver is 25 meters deep underwater.

### 8. Gain and Loss in Stocks

Jack’s investment portfolio lost \$1000, but then he gained \$500. What is his net loss or gain?

Solution

-\$1000 (initial loss) + \$500 (gain) = -\$500

Jack’s net loss is -\$500.

Word problems like these help reinforce the understanding of negative number addition and subtraction by applying them to real-life situations. Practice solving various scenarios to build confidence and proficiency in handling negative numbers.

## Word Problems On Negative Number Addition And Subtraction FAQS

#### Why do negative numbers matter in mathematics?

Negative numbers represent values that are less than zero and are essential in various real-life situations such as temperature, debt, and coordinates in geometry. Understanding negative numbers expands the scope of mathematical operations and problem-solving abilities.

#### How do you add negative numbers?

• If you’re adding two negative numbers, you add their absolute values and keep the negative sign.
• If you’re adding a negative number and a positive number, treat it as subtracting the absolute value of the negative number from the positive number.

#### How do you subtract negative numbers?

When subtracting negative numbers:

• You can treat it as adding the absolute value of the negative number.
• If subtracting a negative number, it’s equivalent to adding a positive number.

#### Why does subtracting a negative number result in addition?

Subtraction of a negative number is essentially the same as addition because subtracting a negative is equivalent to adding a positive. This concept arises from the rules of arithmetic and helps simplify calculations involving negative numbers.

#### Can you give real-life examples of negative number addition and subtraction?

• Temperature changes: A drop in temperature from 3°C to -5°C involves subtraction.
• Financial transactions: Adding or subtracting expenses and income, such as paying off debts or receiving payments.
• Elevator movements: Going up or down floors, where descending involves subtracting from the current floor number.

#### How can I become proficient in negative number addition and subtraction?

• Understand the rules thoroughly, especially regarding the signs of the numbers.
• Practice with a variety of examples, including word problems, to apply the concepts in different contexts.
• Visualize number lines or use other strategies to conceptualize the operations.
• Seek help from teachers, tutors, or online resources if you encounter challenges.

#### Can negative numbers be added or subtracted with positive numbers?

Yes, negative numbers can be added or subtracted with positive numbers. The rules for addition and subtraction remain consistent regardless of the signs of the numbers involved.

#### How do negative number operations relate to other mathematical concepts?

Negative number operations are foundational in algebra, geometry, calculus, and many other branches of mathematics. They are used extensively in equations, inequalities, coordinates, vectors, and various mathematical models.

#### What are some common mistakes to avoid when working with negative numbers?

• Misinterpreting the signs: Ensure you understand whether a number is positive or negative in each context.
• Forgetting to apply the rules: Remember the rules for adding and subtracting negative numbers and apply them correctly.
• Not considering the magnitudes: Pay attention to the absolute values of numbers when performing operations.

#### Where can I find additional resources to practice negative number addition and subtraction?

You can find worksheets, online exercises, math textbooks, and educational websites that offer practice problems and tutorials specifically focused on negative number operations. Additionally, many math apps and games include sections dedicated to practicing arithmetic with 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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