Give A Real-life Situation For The Product $4 \cdot (-2)$.

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Understanding the Concept of Negative Numbers

In mathematics, negative numbers are used to represent quantities that are less than zero. They are often used to describe situations where there is a loss or a decrease. For example, if you have -$10 in your bank account, it means you owe $10 to the bank.

A Real-Life Situation for the Product 4⋅(−2)4 \cdot (-2)

Let's consider a real-life situation where the product 4⋅(−2)4 \cdot (-2) is used.

Tom's Bank Account

Tom has a bank account with a balance of $-20. He receives a refund of $8 from a store he returned some items to. He also receives a payment of $12 from a friend who owes him money. However, he has to pay a fine of $4 for a traffic ticket.

Calculating the New Balance

To calculate Tom's new balance, we need to add the refund and the payment, and then subtract the fine. We can represent this situation using the product 4⋅(−2)4 \cdot (-2).

Step 1: Add the Refund and the Payment

The refund is $8 and the payment is $12, so we add them together:

$8 + $12 = $20

Step 2: Subtract the Fine

The fine is $4, so we subtract it from the total:

$20 - $4 = $16

Step 3: Calculate the New Balance

Tom's initial balance was $-20. We added $20 to it, and then subtracted $4, so we need to multiply $4 by $-2 to get the correct result:

$4 \cdot (-2) = -$8

The Final Answer

Tom's new balance is $-8.

Conclusion

In this real-life situation, the product 4⋅(−2)4 \cdot (-2) is used to calculate Tom's new balance after receiving a refund, a payment, and paying a fine. The result is a negative number, which represents a decrease in Tom's bank account balance.

Real-Life Applications of Multiplication of Negative Numbers

Multiplication of negative numbers has many real-life applications, including:

  • Finance: When calculating interest rates, fees, and refunds, negative numbers are used to represent losses or decreases.
  • Science: In physics, negative numbers are used to represent energy levels, temperatures, and other quantities that can be less than zero.
  • Economics: In economics, negative numbers are used to represent losses, decreases in production, and other economic indicators.

Common Misconceptions about Multiplication of Negative Numbers

Many people believe that multiplying two negative numbers together will result in a positive number. However, this is not true. When multiplying two negative numbers together, the result is always a negative number.

Tips for Understanding Multiplication of Negative Numbers

To understand multiplication of negative numbers, follow these tips:

  • Use real-life examples: Use real-life situations to illustrate the concept of multiplication of negative numbers.
  • Visualize the concept: Use diagrams and charts to visualize the concept of multiplication of negative numbers.
  • Practice, practice, practice: Practice multiplying negative numbers to become more comfortable with the concept.

Conclusion

Q: What is the rule for multiplying two negative numbers together?

A: When multiplying two negative numbers together, the result is always a positive number.

Q: Why is this rule true?

A: This rule is true because when you multiply two negative numbers together, you are essentially multiplying two quantities that are less than zero. This results in a positive quantity, which represents a gain or an increase.

Q: Can you give an example of multiplying two negative numbers together?

A: Yes, here is an example:

(−3)⋅(−4)=12(-3) \cdot (-4) = 12

In this example, we multiplied two negative numbers together and got a positive result.

Q: What is the rule for multiplying a negative number and a positive number together?

A: When multiplying a negative number and a positive number together, the result is always a negative number.

Q: Why is this rule true?

A: This rule is true because when you multiply a negative number and a positive number together, you are essentially multiplying a quantity that is less than zero by a quantity that is greater than zero. This results in a negative quantity, which represents a loss or a decrease.

Q: Can you give an example of multiplying a negative number and a positive number together?

A: Yes, here is an example:

(−5)⋅3=−15(-5) \cdot 3 = -15

In this example, we multiplied a negative number and a positive number together and got a negative result.

Q: How do I remember the rules for multiplying negative numbers?

A: One way to remember the rules is to use the following mnemonic device:

  • When multiplying two negative numbers together, think of it as "two negatives make a positive".
  • When multiplying a negative number and a positive number together, think of it as "a negative and a positive make a negative".

Q: Can you give me some practice problems to help me understand multiplication of negative numbers?

A: Yes, here are some practice problems:

  1. (−2)⋅(−3)=?(-2) \cdot (-3) = ?
  2. (−4)⋅2=?(-4) \cdot 2 = ?
  3. (−6)⋅(−1)=?(-6) \cdot (-1) = ?
  4. (−8)⋅3=?(-8) \cdot 3 = ?
  5. (−10)⋅(−2)=?(-10) \cdot (-2) = ?

Answer Key

  1. 66
  2. −8-8
  3. 66
  4. −24-24
  5. 2020

Conclusion

In conclusion, multiplication of negative numbers is a fundamental concept in mathematics that can be used to solve a wide range of problems. By understanding the rules for multiplying negative numbers, you can better analyze and solve real-life problems. Remember to use the mnemonic device "two negatives make a positive" and "a negative and a positive make a negative" to help you remember the rules. With practice and patience, you will become more comfortable with multiplication of negative numbers and be able to apply it to a variety of situations.