Word Problems on Multiplying And Dividing Negative Numbers

Multiplying and Dividing Negative Numbers: Understanding the Basics

In the realm of mathematics, negative numbers often pose unique challenges for students. However, once you grasp the fundamental rules governing the multiplication and division of negative numbers, you’ll find that they follow a logical pattern.

Let’s delve into these operations and unravel their mysteries.

Multiplying Negative Numbers

When you multiply two negative numbers together, the result is always positive. This might seem counterintuitive at first, but it aligns with the concept of opposite signs canceling each other out.

For example:

(-2) * (-3) = 6

(-5) * (-4) = 20

(-8) * (-6) = 48

In each case, multiplying two negative numbers yields a positive product.

Multiplying Negative and Positive Numbers

When you multiply a negative number by a positive number, the result is always negative. This occurs because the negative sign signifies a direction opposite to the positive.

For example:

(-2) * 3 = -6

(-5) * 2 = -10

(-8) * 7 = -56

In each case, multiplying a negative number by a positive number yields a negative product.

Dividing Negative Numbers

Dividing negative numbers follows similar rules to multiplication. The result is positive when you divide two negative numbers or a negative number by a positive number. This is because division is essentially the inverse operation of multiplication.

For example:

(-6) ÷ (-2) = 3
(-12) ÷ (-3) = 4
(-15) ÷ 5 = -3

In each case, dividing two negative numbers or a negative number by a positive number yields a positive quotient.

Dividing Negative and Positive Numbers

Conversely, the result is always negative when you divide a negative number by a positive number. This is because division by a positive number results in a direction opposite to the original negative value.

For example:

(-8) ÷ 2 = -4

(-10) ÷ 5 = -2

(-24) ÷ 6 = -4

In each case, dividing a negative number by a positive number yields a negative quotient.

Word Problems

Multiplying Negative Numbers

1. Temperature Change:

Imagine you’re in a city where the temperature drops by 5 degrees Celsius each hour. If the temperature is currently at -3 degrees Celsius, what will it be after 4 hours? 

Solution:

-3 (current temperature) – (5 * 4) = -3 – 20 = -23 degrees Celsius.

So, after 4 hours, the temperature will be -23 degrees Celsius.

2. Debt Increase:

You owe $50 to a friend, and your debt increases by $10 each day. If your current debt is -$50, what will it be after 3 days?

 Solution:

-50 (current debt) + (10 * 3) = -50 + 30 = -$20.

After 3 days, your debt will be -$20.

3. Losses in Business:

A business experiences a loss of $200 each week. If the current loss is -$800, what will it be after 5 weeks?

Solution:

-800 (current loss) + (-200 * 5) = -800 – 1000 = -$1800.

After 5 weeks, the loss will be -$1800.

Dividing Negative Numbers

1. Sharing Debts:

You have a debt of -$100, and you want to share it equally among 5 friends. How much debt will each friend have?

Solution:

-100 (total debt) ÷ 5 = -$20.

Each friend will have a debt of -$20.

2. Budget Allocation:

A budget of -$500 needs to be divided among 4 departments equally. What is the budget for each department?

Solution:

-500 (total budget) ÷ 4 = -$125.

Each department will have a budget of -$125.

3. Distributing Losses:

A company experiences a total loss of -$1500, which is distributed equally among 6 partners. How much loss does each partner bear?

Solution:

-1500 (total loss) ÷ 6 = -$250.

Each partner bears a loss of -$250.

Remember, when dealing with negative numbers:

• Multiplying or dividing two negative numbers results in a positive number.
• Multiplying a negative number by a positive number yields a negative result.
• Dividing a negative number by a positive number yields a negative result.

Word Problems on Multiplying And Dividing Negative Numbers FAQS

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