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Algebra for Kids2 chapters | 6 lessons

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Lesson Transcript

Instructor:
*Nola Bridgens*

Nola has taught elementary school and tutored for four years. She has a bachelor's degree in Elementary Education, a master's degree in Marketing, and is a certified teacher.

In this lesson, learn the rules for dealing with negative fractions as well as five simple steps to divide negative fractions. We also discuss practical uses for this skill.

When you hear the word 'negative,' do you get a bad feeling? While 'negative' can sometimes indicate that something is not good, that is not what it means in math. In fact, this lesson is going to be 'positively' awesome as you go scuba diving and chase a storm while learning how to divide negative fractions. Now that doesn't sound bad, does it?

Before we start on our adventures, there are some rules we have to review. The first set of rules deals with mixing positive and negative signs.

It is really quite easy:

If the signs are the *same* (either both positive or both negative), then the answer is positive.

If the signs are *different* (one negative and one positive), the answer is negative.

One more set of rules and we will be on our way!

Dividing fractions is the same thing as multiplying by a reciprocal fraction. A **reciprocal** is when you take a fraction and have the numerator and denominator switch places. For example, the reciprocal of 2/3 is 3/2. You must remember, however, that it is *always* the **divisor**, the number that is doing the actual work of dividing, that gets flipped. In division problems, the divisor is the second fraction.

Here are our steps for dividing fractions:

- Find the reciprocal of the divisor, or second fraction.
- Multiply the numerators together
- Multiply the denominators together
- Simplify the answer if possible
- Determine if the answer is positive or negative using the sign rules

OK. Now it is time to chase a storm!

As a storm chaser, you are following Hurricane David and you notice a significant decrease in temperature. The current temperature has dropped a total of -2/3 degrees in the last 10 minutes! You need to report how much the temperature is dropping every minute. To find out, you need to divide the total temperature drop (-2/3 degrees) by how many minutes it took (10).

Your problem looks like this: -2/3 ÷ 10. Now, let's go through the steps to solve.

1. Find the reciprocal of the second fraction.

- We can change 10 into a fraction by placing it over 1: 10/1. The reciprocal is 1/10.

2. Multiply numerators: 2 x 1 = 2

3. Multiply denominators: 3 x 10 = 30

4. Simplify 2/30 to 1/15 (they are both divisible by 2)

5. One fraction is positive and one is negative, so the signs are *different* and the answer is negative.

Therefore, the temperature is dropping - 1/15 of a degree every minute.

Now, let's say you are a scuba diver and must dive a total of -3/4 km to reach the ocean floor. However, for safety reasons, you must stop six times to check your equipment during your dive. If you want to stop at equal intervals, how often do you need to stop? We need to divide the total distance you need to dive (-3/4 km) by how many times you need to stop (6) to get our answer.

Your problem looks like this: -3/4 ÷ 6.

1. Find the reciprocal of the second fraction.

- We can change 6 into a fraction by placing it over 1: 6/1. The reciprocal is 1/6.

2. Multiply numerators: 3 x 1 = 3

3. Multiply denominators: 4 x 6 = 24

4. Simplify 3/24 to 1/8 (they are both divisible by 3)

5. One fraction is positive and one is negative, so the signs are *different* and the answer is negative.

You need to stop every -1/8 of a km to check your equipment.

Easy! See, nothing 'negative' about dividing negative fractions!

Let's take a brief moment to review what we've learned about diving negative fractions.

Dividing negative fractions involves finding the reciprocal of the divisor. The **reciprocal** is found by having the numerator and the denominator switch places. The **divisor** is the number that is doing the actual work of dividing. Is is the second fraction. We then multiply the first fraction by the reciprocal of the second fraction. When fractions have the same signs, the answer will be positive; when fractions have different signs, the answer will be negative.

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Algebra for Kids2 chapters | 6 lessons

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