Adding and Subtracting Positive and Negative Numbers

Adding and subtracting positive and negative numbers is a fundamental concept in mathematics, particularly in the study of integers. Understanding how to work with these numbers is crucial for solving a wide range of mathematical problems and real-life situations.

What are Integers?

Integers are a set of numbers that include all whole numbers and their opposites. This means integers consist of:

• Positive numbers (e.g., 1, 2, 3, ...)
• Negative numbers (e.g., -7, -9, -3, ...)
• Zero (0)

Integers do not include fractions or decimals. They are represented on a number line, where positive numbers are to the right of zero, and negative numbers are to the left of zero.

Positive and Negative Numbers

Positive numbers are numbers greater than zero. They represent quantities that are above a baseline or in a gain.

Negative numbers are numbers less than zero. They represent quantities below a baseline or in a loss.

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Strategy to Add Positive and Negative Numbers

When adding positive and negative numbers, the key is to understand the effect of the signs:

• Example: 7 + 5 = 12

2. Adding Two Negative Numbers: Add their absolute values and give the sum a negative sign.

• Example: (−7) + (−5) = −12

3. Adding a Positive Number and a Negative Number: Subtract the smaller absolute value from the larger absolute value and give the result the sign of the number with the larger absolute value.

• Example: 7 + (−5) = 2

• Example: (−7) + 5 = −2

Strategy to Subtract Positive and Negative Numbers

When subtracting positive and negative numbers, it's helpful to rewrite the problem as an addition problem:

1. Subtracting Two Positive Numbers: Subtract their absolute values.

• Example: 7 – 5 = 2

2. Subtracting Two Negative Numbers: Subtract the absolute values of the numbers and give the result the sign of the number with the larger absolute value.

• Example: (−7) − (−5) = −2

3. Subtracting a Positive Number and a Negative Number: Add the absolute value of the second number to the first number.

• Example: 7− (−5) = 12

4. Subtracting a Negative Number from a Positive Number: Add the absolute value of the second number to the first number.

• Example: (−7) – 5 = −12

Real-Life Word Problems with Solutions

Problem 1: The temperature at midnight was -7°C. By noon, the temperature rose by 12°C. What is the temperature at noon?

Solution: −7 + 12 = 5 The temperature at noon is 7°C.

Problem 2: Alex had \$500 in his bank account. He withdrew \$200 for a purchase. What is his account balance now?

Solution: 500 – 200 = −300 Alex's account balance is -\$300.

Problem 5: A hiker starts at an elevation of 500 meters. She ascends 240 meters and then descends 100 meters. What is her final elevation?

Solution: 500 + 240 – 100 = 640 Her final elevation is 640 meters.

Problem 4: A stock initially valued at \$100 per share increases by \$20, and then decreases by \$57. What is the final value of the stock?

Solution: 100 + 20 – 57 = 63 The final value of the stock is \$63 per share.

Adding and subtracting positive and negative numbers is a vital skill that extends beyond the classroom to everyday life. By mastering these concepts, you can solve a wide range of problems, from managing finances to understanding elevation changes. Practice with real-life examples to enhance your understanding and application of these fundamental mathematical operations.

Q.1: What are the basic rules for adding positive and negative numbers?

Ans: The basic rules for adding positive and negative numbers are:

• Adding two positive numbers: Simply add their values (e.g., 7 + 5 = 12).
• Adding two negative numbers: Add their absolute values and give the sum a negative sign (e.g., (−7) + (−5) = −12.
• Adding a positive number and a negative number: Find the absolute values, then Subtract the smaller absolute value from the larger absolute value, and then give the result the sign of the number with the larger absolute value (e.g., 7 + (−5) = 2.

Q.2: How do you subtract a positive number from a negative number?

Ans: When subtracting a positive number from a negative number, add the absolute value of the positive number to the negative number:

Example: (−8) – 9 = −17.

Q.3: What happens when you subtract a negative number from a positive number?

Ans: Subtracting a negative number from a positive number is equivalent to adding the absolute value of the negative number to the positive number:

Example: 7 − (−8) = 7 + 8 = 15.

Q.4: How can understanding positive and negative numbers help in real-life situations?

Ans: Understanding positive and negative numbers is crucial for managing finances (e.g., calculating bank balances), tracking temperature changes, understanding elevations and depths, and analyzing gains and losses in investments.

Q.5: Can you provide an example where adding and subtracting positive and negative numbers is used in a practical scenario?

Ans:

• If you have \$170 in your bank account (positive balance) and you make a purchase of \$200 (withdrawal, negative impact), you would calculate your new balance by subtracting \$200 from \$170: 170−200 = −30
• This means your new balance is -\$30, indicating an overdraft.

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