Forgetting to multiply the negative signs

Oct 13, 2025 by leolavanderia.com.br 140 views

Understanding the Problem

When dealing with fractions, multiplying them can be a bit tricky, especially when one or both of the fractions are negative. In this article, we will explore how to multiply negative fractions, using the example of -2/9 × —5/3.

What are Negative Fractions?

A negative fraction is a fraction that has a negative sign in front of it. For example, -2/9 is a negative fraction, as is —5/3. When multiplying negative fractions, we need to remember that a negative times a negative is a positive.

Multiplying Fractions: A Review

Before we dive into multiplying negative fractions, let's review how to multiply fractions in general. To multiply fractions, we simply multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), and then simplify the result.

Multiplying Negative Fractions: The Step-by-Step Process

Now that we have reviewed how to multiply fractions, let's apply this knowledge to the example of -2/9 × —5/3.

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply the numbers on top. In this case, we have -2 and —5. Multiplying these numbers gives us:

-2 × —5 = 10

Step 2: Multiply the Denominators

To multiply the denominators, we simply multiply the numbers on the bottom. In this case, we have 9 and 3. Multiplying these numbers gives us:

9 × 3 = 27

Step 3: Write the Result as a Fraction

Now that we have multiplied the numerators and denominators, we can write the result as a fraction. In this case, we have:

10/27

Step 4: Simplify the Result (If Necessary)

In this case, the result is already simplified, so we don't need to do anything further.

The Final Answer

So, what is the final answer to the problem -2/9 × —5/3? The answer is:

10/27

Conclusion

Multiplying negative fractions may seem intimidating at first, but with a step-by-step approach, it's actually quite straightforward. By following the steps outlined in this article, you should be able to multiply negative fractions with ease.

Common Mistakes to Avoid

When multiplying negative fractions, there are a few common mistakes to avoid. These include:

Forgetting to multiply the negative signs: When multiplying negative fractions, it's essential to remember that a negative times a negative is a positive.
Not simplifying the result: Make sure to simplify the result of the multiplication, if possible.
Getting the signs wrong: Double-check that you have the correct signs in your answer.

Practice Problems

To help you practice multiplying negative fractions, here are a few example problems:

-3/4 × —2/5
2/3 × —5/6
-1/2 × —3/4

Try solving these problems on your own, and then check your answers against the solutions provided below.

Solutions

-3/4 × —2/5 = 6/20 = 3/10
2/3 × —5/6 = -10/18 = -5/9
-1/2 × —3/4 = 3/8

Conclusion

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about multiplying negative fractions.

Q: What is the rule for multiplying negative fractions?

A: The rule for multiplying negative fractions is that a negative times a negative is a positive. This means that when you multiply two negative fractions, the result will be a positive fraction.

Q: How do I multiply fractions with different signs?

A: When multiplying fractions with different signs, you need to remember that a negative times a positive is a negative. For example, -2/3 × 4/5 = -8/15.

Q: Can I simplify the result of multiplying fractions?

A: Yes, you can simplify the result of multiplying fractions. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the largest factor that they have in common.

Q: Can I use a calculator to multiply fractions?

A: Yes, you can use a calculator to multiply fractions. However, it's always a good idea to check your answer by multiplying the fractions by hand.

Q: What are some common mistakes to avoid when multiplying fractions?

A: Some common mistakes to avoid when multiplying fractions include:

Forgetting to multiply the negative signs
Not simplifying the result
Getting the signs wrong
Not using the correct order of operations

Q: Can I multiply fractions with zero?

A: Yes, you can multiply fractions with zero. However, the result will be zero.

Q: What is the result of multiplying a fraction by zero?

A: The result of multiplying a fraction by zero is zero.

Q: Can I multiply fractions with negative exponents?

A: Yes, you can multiply fractions with negative exponents. However, you need to remember that a negative exponent means that the fraction is being raised to a power.

Q: How do I multiply fractions with negative exponents?

A: To multiply fractions with negative exponents, you need to remember that a negative exponent means that the fraction is being raised to a power. For example, (2/3)^(-2) = 9/4.

Conclusion

Multiplying negative fractions can be a bit tricky, but with practice and patience, you should be able to master this skill. Remember to follow the rules outlined in this article, and don't be afraid to ask for help if you need it. Happy multiplying!

Practice Problems

To help you practice multiplying negative fractions, here are a few example problems:

-3/4 × —2/5
2/3 × —5/6
-1/2 × —3/4
(2/3)^(-2)
(4/5)^(-3)

Try solving these problems on your own, and then check your answers against the solutions provided below.

Solutions

-3/4 × —2/5 = 6/20 = 3/10
2/3 × —5/6 = -10/18 = -5/9
-1/2 × —3/4 = 3/8
(2/3)^(-2) = 9/4
(4/5)^(-3) = 125/64