Fraction Multiplication: Step-by-Step Solutions

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Hey guys! Let's dive into the world of fraction multiplication with these two problems. We'll break it down step by step, so you can ace these types of questions. Get ready to sharpen your math skills!

Problem 1: Multiplying 7/10 by 3

So, our first task is to figure out what happens when we multiply the fraction 7/10 by the whole number 3. Don't worry, it's simpler than it looks! When you're multiplying a fraction by a whole number, think of the whole number as a fraction with a denominator of 1. In this case, 3 becomes 3/1. This little trick makes the multiplication process super straightforward.

Now, we have 7/10 multiplied by 3/1. To multiply fractions, you just multiply the numerators (the top numbers) together and then multiply the denominators (the bottom numbers) together. So, we're doing 7 times 3 for the new numerator and 10 times 1 for the new denominator. This gives us 21/10. Awesome, right?

But wait, we're not quite done yet! The fraction 21/10 is what we call an improper fraction because the numerator (21) is bigger than the denominator (10). To make it look nicer and easier to understand, we need to convert it into a mixed number. A mixed number has a whole number part and a fraction part. To convert, we see how many times 10 goes into 21. It goes in 2 times, with a remainder of 1. So, the whole number part is 2, and the remainder 1 becomes the numerator of our new fraction, keeping the original denominator of 10. Ta-da! We get 2 1/10. This means the correct answer is A) 2 1/10.

Remember, guys, the key is to turn that whole number into a fraction, multiply straight across, and then simplify if you have an improper fraction. You've got this!

Breaking Down the Steps:

  1. Convert the whole number to a fraction: Think of 3 as 3/1.
  2. Multiply the numerators: 7 * 3 = 21
  3. Multiply the denominators: 10 * 1 = 10
  4. Write the new fraction: 21/10
  5. Convert to a mixed number (if needed): 21/10 = 2 1/10

Problem 2: Multiplying 8/13 by 9

Alright, let's tackle another one! This time, we need to multiply the fraction 8/13 by the whole number 9. Just like before, we're going to turn that whole number into a fraction. So, 9 becomes 9/1. You guys are getting the hang of this, right?

Now we have 8/13 multiplied by 9/1. Remember the rule: multiply the numerators together and multiply the denominators together. So, we calculate 8 times 9 for the numerator and 13 times 1 for the denominator. This gives us 72/13. Sweet!

But guess what? We've got another improper fraction on our hands! 72/13 means we need to convert it into a mixed number. Let's figure out how many times 13 goes into 72. If you think about it, 13 goes into 72 five times (since 13 times 5 is 65), with a remainder of 7. So, our whole number part is 5, and the remainder 7 becomes the numerator of our new fraction, keeping the denominator 13. We end up with 5 7/13. That means the correct answer is B) 5 7/13.

See, guys? These problems are totally manageable when you break them down into smaller steps. Keep practicing, and you'll be a fraction multiplication pro in no time!

Steps in Action:

  1. Convert the whole number to a fraction: 9 becomes 9/1.
  2. Multiply the numerators: 8 * 9 = 72
  3. Multiply the denominators: 13 * 1 = 13
  4. Write the new fraction: 72/13
  5. Convert to a mixed number (if needed): 72/13 = 5 7/13

Key Concepts in Fraction Multiplication

Converting Whole Numbers to Fractions

One of the first key concepts in multiplying fractions with whole numbers is understanding how to represent a whole number as a fraction. Guys, this is super simple! Any whole number can be written as a fraction by placing it over a denominator of 1. For example, the number 5 can be written as 5/1. This works because any number divided by 1 is itself. When you're faced with a problem like multiplying a fraction by a whole number, this little trick is essential. It makes the multiplication process much clearer and easier to manage. So, always remember, when you see a whole number, think of it as a fraction with 1 as the denominator. This makes the rest of the process flow smoothly. You've got this!

Multiplying Numerators and Denominators

Now, let's talk about the core mechanic of multiplying fractions: multiplying the numerators and the denominators. This is the heart of fraction multiplication, and it's really straightforward once you get the hang of it. The numerator is the top number in a fraction, and the denominator is the bottom number. When you multiply fractions, you simply multiply the numerators together to get the new numerator, and you multiply the denominators together to get the new denominator. For example, if you're multiplying 2/3 by 4/5, you multiply 2 times 4 to get 8 (the new numerator) and 3 times 5 to get 15 (the new denominator). This gives you the new fraction 8/15. Remember this simple rule, and you'll nail fraction multiplication every time. It's all about multiplying straight across!

Converting Improper Fractions to Mixed Numbers

Alright, let's chat about what happens when our fractions get a little too big – we're talking about improper fractions! An improper fraction is when the numerator (the top number) is larger than the denominator (the bottom number). While there's nothing mathematically wrong with them, they're not always the easiest to understand at a glance. That's where mixed numbers come in! A mixed number is a combination of a whole number and a proper fraction (where the numerator is smaller than the denominator). Think of it like this: 7/2 is an improper fraction, but it can be rewritten as the mixed number 3 1/2. See how much clearer that is? To convert an improper fraction to a mixed number, you divide the numerator by the denominator. The quotient (the whole number part of your answer) becomes the whole number in the mixed number. The remainder becomes the numerator of the fraction, and you keep the original denominator. This skill is super useful for simplifying your answers and making them easier to understand. So, master this, and you'll be a fraction whiz in no time!

Practice Makes Perfect

Guys, the best way to get comfortable with multiplying fractions is to practice, practice, practice! Try making up your own problems or finding some online. Work through them step by step, and don't be afraid to make mistakes – that's how you learn! The more you practice, the more confident you'll become.

Keep Learning!

Multiplying fractions is a foundational skill in math. Once you've mastered it, you'll be ready to tackle even more challenging concepts. So keep up the great work, and happy multiplying!