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ELM: CSU Math Study Guide16 chapters | 140 lessons

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Lesson Transcript

Instructor:
*Jeff Calareso*

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Adding whole numbers is one thing. But adding fractions and mixed numbers? That's not so simple. Or is it? In this lesson, we'll practice arithmetic with both fractions and mixed numbers.

Fashion styles come and go, but there are certain fashion rules that never change. And you don't have to be a fashion expert to know some of these. For example, socks and sandals? Super comfortable, but not okay. Stripes and plaid? Don't do that. Vertical and horizontal stripes? That's just weird.

Fractions operate in much the same way. Depending on what you're trying to do with your fractions, you may need to color-coordinate. But sometimes you can just pick any two fractions and you're okay. It's all about the operation you're trying to perform. Let's work on practicing arithmetic with fractions and mixed numbers. First, though, let's quickly review what we're talking about.

A **fraction** is simply a part of a whole number. 1/2, 3/4, 25/26 - these are fractions. 26/26 would just be simplified to 1, which is not a fraction. Fractions consist of two parts, a numerator (which is the top number) and a denominator (which is the bottom number). A **mixed number** is a whole number and a fraction. Let's say you had 3/2. You could simplify that to 1 1/2. That's a mixed number. Okay, let's practice!

Let's start with **multiplication**. This is the easiest fraction operation. We just multiply the numerators, then multiply the denominators. It's like our closet only has matching colors.

So, 1/2 * 1/4 is just 1/8. 2/3 * 3/7? That's 6/21. 5/6 * 7/8? That's 35/48. When you multiply fractions, people are jealous of how good you look no matter what you wear.

Sometimes you need to do a little simplifying at the end. If you multiply 3/4 * 2/3, you get 6/12. That simplifies to 1/2.

With mixed numbers, we can follow the same process, but we first have to convert to an improper fraction. This just means multiplying the whole number times the denominator, then adding it to the numerator. So 1 1/2 becomes 3/2. 3 2/3 becomes 11/3. This is like working with more colors, though maybe they're all Earth tones, so they kind of all still go together.

So what is 4 1/2 * 2 3/4? 4 1/2 becomes 9/2 and 2 3/4 becomes 11/4. 9/2 * 11/4 is 99/8. We then convert that back to a mixed number by reversing the process we did before: divide the numerator by the denominator. The answer becomes the whole number and the remainder becomes the numerator. So we have 12 3/8.

What about 1 1/5 * 1 1/6? 1 1/5 becomes 6/5 and 1 1/6 becomes 7/6. 6/5 * 7/6 is 42/30, or 1 12/30. We can simplify that to 1 2/5.

If you want to add or subtract fractions, you need to abide by the fashion police. You can't just add 1/2 to 1/4. That's like going out wearing two kinds of plaid. You're not in a '90s grunge band, are you?

So we need to coordinate. To do that, we need to get the same denominator on both fractions. If we want to add 1/4 and 1/4, we just add the numerators and get 2/4. With 1/2 and 1/4, we need to find the least common denominator, which is 4. We multiply 1/2 * 2/2 to get 2/4. Now we can add them to get 3/4.

What about 3/5 + 2/3? The least common denominator is 15. So we multiply 3/5 * 3/3 to get 9/15. We multiply 2/3 * 5/5 to get 10/15. 9/15 + 10/15 is 19/15. That can be simplified to 1 4/15.

**Subtraction** works the same. We still can't wear that purple shirt with the neon green pants. Why do we have neon green pants, anyway? Oh, but subtraction practice.

What is 5/6 - 1/3? The least common denominator is 6, so we convert 1/3 to 2/6. 5/6 - 2/6 is 3/6, or 1/2.

What about 1/2 - 7/8? 8 is our least common denominator, so 1/2 becomes 4/8. 4/8 - 7/8 is -3/8.

With mixed numbers, it's simplest to convert to improper fractions. So for 3 1/3 - 2 1/2, we convert 3 1/3 to 10/3 and 2 1/2 to 5/2. 6 is our least common denominator. So 10/3 becomes 20/6. 5/2 becomes 15/6. 20/6 - 15/6 is 5/6.

What about 7 1/4 + 5 4/5? 7 1/4 becomes 29/4. 5 4/5 becomes 29/5. Our least common denominator is 20. So 29/4 becomes 145/20. 29/5 becomes 116/20. Add them together and we have 261/20, which is 13 1/20.

Finally, there's dividing fractions. This is for fashion pioneers. When we divide fractions, we turn the second fraction upside down and then multiply the fractions together. It's like the crazy stuff you see at those fancy fashion shows. Is she wearing pants on her head? Are those sunglasses on her knees?

So with (1/2) / (4/5), we turn 4/5 upside down to 5/4, which is its reciprocal. Then we do 1/2 * 5/4, which is 5/8.

What about (5/6) / (3/8)? 3/8 becomes 8/3. And 5/6 * 8/3 is 40/18. We can simplify that to 20/9, or 2 2/9.

**Dividing mixed numbers** is just like multiplying. We just need to first convert them to improper fractions.

So (2 2/3) / (1 1/2)? 2 2/3 becomes 8/3. And 1 1/2 becomes 3/2. The reciprocal of 3/2 is 2/3. And 8/3 * 2/3 is 16/9. That simplifies to 1 7/9.

What about (4 3/4) / (2 1/5)? 4 3/4 becomes 19/4. 2 1/5 becomes 11/5. We flip 11/5 to get 5/11. And 19/4 * 5/11 is 95/44. That converts to 2 7/44.

In summary, **multiplying** fractions involves just multiplying the numerators by each other, then the denominators. **Adding and subtracting** requires us to find the least common denominator. Then we just add or subtract the numerators. With division, we're in high fashion territory. We flip the second **fraction** to its reciprocal. Then we multiply them together. When we have **mixed numbers**, we convert them to improper fractions. And no matter what, no socks with sandals! I'm serious about that.

After watching this lesson, you might be able to apply basic arithmetic skills (addition/subtraction, multiplication/division) when solving problems with fractions and mixed numbers.

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ELM: CSU Math Study Guide16 chapters | 140 lessons

- How to Build and Reduce Fractions 3:55
- How to Find Least Common Denominators 4:30
- Comparing and Ordering Fractions 7:33
- Changing Between Improper Fraction and Mixed Number Form 4:55
- How to Add and Subtract Like Fractions and Mixed Numbers 4:14
- How to Add and Subtract Unlike Fractions and Mixed Numbers 6:46
- Multiplying Fractions and Mixed Numbers 7:23
- Dividing Fractions and Mixed Numbers 7:12
- Practice with Fraction and Mixed Number Arithmetic 7:50
- Solving Problems using Fractions and Mixed Numbers 7:08
- How to Solve Complex Fractions 5:20
- Calculations with Ratios and Proportions 5:35
- Using Proportions to Solve Ratio Problems
- Practice Problems for Calculating Ratios and Proportions 5:59
- Go to ELM Test - Numbers and Data: Rational Numbers

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