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# 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.

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## 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.

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## 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

#### What are negative numbers?

Negative numbers are real numbers that are less than zero. They represent values that are below a reference point, often denoted by a negative sign (-).

#### How do you multiply negative numbers?

When multiplying negative numbers:

• If you multiply two negative numbers together, the result is positive.
• If you multiply a negative number by a positive number, the result is negative.

#### How do you divide negative numbers?

When dividing negative numbers:

• The result is positive if you divide two negative numbers or a negative number by a positive number.
• The result is negative if you divide a negative number by a positive number.

#### Why does multiplying two negative numbers result in a positive number?

Multiplying two negative numbers results in a positive number because they represent opposite directions or movements along a number line. When you multiply opposites, they cancel each other out, yielding a positive result.

#### What are some real-world examples of multiplying and dividing negative numbers?

• Multiplying: Calculating temperature changes (e.g., if the temperature decreases by -5°C each hour, what will it be after 4 hours?)
• Dividing: Sharing debts among friends (e.g., if you owe -\$100 and split it among 5 friends, how much does each owe?)

#### How can I practice multiplying and dividing negative numbers?

You can practice with worksheets, and online exercises, or create your own word problems. Additionally, applying these concepts to real-life scenarios helps reinforce understanding.

#### What are some tips for mastering negative number operations?

• Understand the rules thoroughly.
• Practice regularly with various types of problems.
• Use real-world examples to relate concepts to everyday life.
• Seek help from teachers, tutors, or online resources if you encounter challenges.

#### Can negative numbers be multiplied or divided by positive numbers?

Yes, negative numbers can be multiplied or divided with positive numbers. The rules for multiplication and division remain the same as mentioned earlier.

#### How do negative numbers affect calculations in algebra and geometry?

Negative numbers are essential in various mathematical concepts. In algebra, they are used in solving equations and inequalities. In geometry, they represent coordinates, distances, and directions.

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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