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

Addition of Negative Numbers:

1. Same Sign Addition

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.

2. Different Sign Addition:

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.

Subtraction of Negative Numbers

1. Subtraction as Addition

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.

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

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