Dividing positive and negative numbers can be challenging, especially with fractions. This article will explain how to divide both positive and negative fractions. In the end, you will understand these topics better, and it will help you get ready for the ACT® WorkKeys Applied Math Test.
What We Review
Understanding the Rules of Dividing Positive and Negative Numbers
Before we start with fractions, let’s review how to divide integers. The rules are simple but important:
- Rule 1: A positive divided by a negative equals a negative.
- Rule 2: A negative divided by a positive also equals a negative.
- Rule 3: Dividing two negative numbers results in a positive number.
These rules explain the basics of whole numbers and fractions and apply to multiplication, too. Understanding these rules makes solving more complex problems simpler.
Applying Division Rules to Fractions
The rules for dividing integers also work for fractions, but there are some differences.
First, check the signs of the fractions. Dividing a positive fraction by a negative fraction gives a negative result.
To divide fractions, flip the divisor and then multiply. This method makes the process easier and the outcome clearer. Careful calculations help avoid common mistakes with fractions.
These guidelines will improve your skills for different challenges, like the ACT® WorkKeys Applied Math test.
Simplifying Fractions Before Dividing Positive and Negative Numbers
When you work with fractions, simplifying them before dividing can make things easier. First, find the greatest common divisor, or GCD, of the top number (numerator) and the bottom number (denominator). The GCD is the largest number that can divide both without leaving a remainder. By simplifying the fraction, you can make the next steps much easier to handle.
Another useful math method is cross-cancellation. This method looks at the numbers in a fraction’s top (numerator) and bottom (denominator) to find factors that can be canceled out before you invert the divisor. This makes multiplying easier and simplifies the division process. Using cross-cancellation can make calculations quicker and less complicated, especially with fractions.
These strategies are useful during exams when time is limited and can lessen mistakes. Get to know them to improve your problem-solving skills.
Multiplying by the Reciprocal: An Alternative Method
To divide fractions, start by flipping the second fraction. This is called taking the reciprocal. After that, multiply the first fraction by the flipped fraction. This method makes dividing fractions simpler. By turning division into multiplication, you can solve it more easily.
Ensure both fractions are simplified before multiplying to avoid mistakes and streamline the process.
This approach is effective, particularly for timed exams.
Practice Problems: Sharpening Your Skills
Practicing division allows you to learn how to divide both negative and positive numbers. Solve various problems to boost your confidence and speed. Here are some practice problems to try.
Practice Problems
Practice Problem 1: Divide -3/4 by 2/5.
To solve the problem of dividing -3/4 by 2/5, we must first remember how division works with fractions. When dividing by a fraction, we can convert the division operation into multiplication by the reciprocal of that fraction.
So, instead of dividing -3/4 by 2/5, we will multiply -3/4 by the reciprocal of 2/5. The reciprocal of 2/5 is 5/2.
Now, we rewrite the equation as follows:
-3/4 \div 2/5 = -3/4 \times 5/2Next, we can multiply the two fractions. We start by multiplying the numerators (the top numbers) together and the denominators (the bottom numbers) together:
Numerator: -3 \times 5 = -15
Denominator: 4 \times 2 = 8
Putting it all together, we have:
-3/4 \div 2/5 = -15/8The final answer is -15/8. This fraction can also be expressed as a mixed number if desired; it is equivalent to -1 and 7/8. Thus, the problem of dividing -3/4 by 2/5 results in -15/8 or -1 7/8.
Practice Problem 2: Divide 6/7 by -3/2.
To solve the problem of dividing the fraction 6/7 by -3/2, we can follow a clear, step-by-step process.
First, it’s important to remember that when we divide by a fraction, we can instead multiply by its reciprocal. Therefore, instead of dividing 6/7 by -3/2, we will multiply 6/7 by the reciprocal of -3/2, which is -2/3.
Now, we can set up the multiplication as follows:
(6/7) \times (-2/3)Next, we multiply the numerators together and the denominators together. For the numerators, we have 6 multiplied by -2, which equals -12. For the denominators, we have 7 multiplied by 3, which equals 21. This gives us the new fraction:
-12/21Finally, we can simplify this fraction if possible. Both -12 and 21 can be divided by 3. When we divide -12 by 3, we get -4, and when we divide 21 by 3, we get 7. Therefore, after simplifying, the final answer is:
-4/7In conclusion, when we divide 6/7 by -3/2, we arrive at the result of -4/7.
Practice Problem 3: Divide -5/9 by -4/3.
In this case, we have -5/9 divided by -4/3. To perform this operation, we take the reciprocal of -4/3, which is -3/4. Now, instead of dividing, we will multiply -5/9 by -3/4.
Next, we carry out the multiplication of the two fractions. To multiply fractions, we multiply the numerators together and then multiply the denominators together. Thus, we multiply -5 (the numerator of the first fraction) by -3 (the numerator of the second fraction) to get 15 as our new numerator. For the denominators, we multiply 9 (the denominator of the first fraction) by 4 (the denominator of the second fraction) to get 36 as our new denominator.
Putting this together, we have 15 as the numerator and 36 as the denominator, resulting in the fraction 15/36.
However, this fraction can be simplified further. Both the numerator and the denominator can be divided by their greatest common divisor, which in this case is 3. Dividing the numerator by 3 gives us 5, and dividing the denominator by 3 gives us 12.
Thus, the final simplified answer to the problem of dividing -5/9 by -4/3 is 5/12.
Once you complete these problems, check your answers for ways to do better. These exercises will help improve your skills before the test.
Common Mistakes in Dividing Positive and Negative Numbers and How to Avoid Them
One common mistake is forgetting the rules for positive and negative signs. Keep in mind which operations produce positive or negative outcomes.
Another mistake is not simplifying fractions when dividing. Simplifying helps make calculations simpler.
To avoid these mistakes, review each step of your work closely. Verify that your results are correct before moving on.
Preparing for the ACT® WorkKeys Applied Math Test
Preparation is crucial for doing well on the ACT® WorkKeys Applied Math Test. You must regularly review and practice different math topics, especially division, including positive and negative numbers. This will help strengthen your understanding of these basic skills, which often appear in various forms on the test.
Managing your time is also key to your study plan. Try using a timer to practice in conditions similar to the actual test. This will help you see how quickly you can answer questions. Practicing with time limits will help you get used to the pace you need during the exam, which can improve your overall performance.
Besides studying independently, using online guides and getting tutoring can be very helpful while you prepare. These resources can give you extra practice and clarify tough topics, like dividing negative and positive numbers or working with fractions. By using these tools, you can better understand the material and feel more confident with the math questions on the ACT® WorkKeys Applied Math Test.
The Importance of Mastering Division
Understanding how to divide positive and negative numbers is essential for success in math. This skill applies to many areas of life and STEM fields. Learning these concepts makes problem-solving easier and supports your performance in exams and daily situations.
Sharpen Your Skills for ACT® WorkKeys Applied Math
Are you preparing for the ACT® WorkKeys Applied Math test? We’ve got you covered! Dive into our review articles designed to help you tackle real-world math problems with confidence. You’ll find everything you need to succeed from quick tips to detailed strategies. Start exploring now!
- Operations with Positive and Negative Numbers
- Adding Positive and Negative Numbers
- Quick Tips for Subtracting Positive and Negative Numbers
- Multiply Positive and Negative Numbers Like a Pro
Need help preparing for the ACT® WorkKeys Applied Math Test?
Albert has hundreds of ACT® WorkKeys practice questions and full-length practice tests to try out.
