Fraction Arithmetic: Step-by-Step Solutions

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Hey guys! Let's break down these fraction problems together. It's all about making math easy and understandable, so you can totally nail it. We'll go through each problem step by step, so grab your pencil and paper, and let's get started!

1. Adding Fractions: 1/10 + 6/10

When you're dealing with fraction addition, the first thing you wanna check is whether the denominators (the bottom numbers) are the same. If they are, you're in luck! It makes everything way simpler. In this case, we're adding 1/10 and 6/10. Notice that both fractions have the same denominator, which is 10.

So, what do we do next? Well, since the denominators are the same, you just add the numerators (the top numbers) together and keep the denominator the same. That means we add 1 and 6.

1 + 6 = 7

Now, put that result over the original denominator, which is 10. So, the answer is:

7/10

And that's it! You've just successfully added two fractions. No need to simplify further since 7 and 10 don't have any common factors other than 1. So, 7/10 is your final answer.

Key Points:

  • Check for Common Denominators: Always make sure the denominators are the same before adding.
  • Add Numerators: Add the top numbers together.
  • Keep Denominator: The denominator stays the same.
  • Simplify: If possible, simplify your final fraction. In this case, 7/10 is already in its simplest form.

2. Adding Fractions: 11/21 + 6/21

Alright, let's jump into another fraction addition problem! This time, we're tackling 11/21 + 6/21. Just like before, the first thing we need to check is whether the denominators are the same. And guess what? They are! Both fractions have a denominator of 21. This makes our job a whole lot easier.

Since the denominators are the same, we can go ahead and add the numerators. We're adding 11 and 6. What does that give us?

11 + 6 = 17

Now, we take that result and put it over the original denominator, which is 21. So, our answer is:

17/21

Now, before we declare victory, we should check if we can simplify the fraction. Simplifying a fraction means reducing it to its lowest terms. To do this, we need to see if there's a common factor between the numerator (17) and the denominator (21). A common factor is a number that divides both the numerator and the denominator evenly.

In this case, 17 is a prime number, which means it's only divisible by 1 and itself. The factors of 21 are 1, 3, 7, and 21. Since 17 and 21 don't share any common factors other than 1, the fraction 17/21 is already in its simplest form. Therefore, our final answer is indeed 17/21.

Key Points:

  • Common Denominators: Verify that the denominators are the same.
  • Add the Numerators: Add the top numbers.
  • Keep the Denominator: The denominator remains the same.
  • Simplify the Fraction: Always check if the fraction can be simplified. Look for common factors between the numerator and the denominator.

3. Subtracting Fractions: 4/19 - 2/19

Now, let's switch gears and dive into fraction subtraction. We're going to solve 4/19 - 2/19. Just like with addition, the first thing we need to check is whether the denominators are the same. In this case, both fractions have a denominator of 19, so we're good to go!

Since the denominators are the same, we can subtract the numerators directly. We're subtracting 2 from 4.

4 - 2 = 2

Now, put that result over the original denominator, which is 19. So, the answer is:

2/19

Before we finalize our answer, we need to check if we can simplify the fraction. To simplify, we look for common factors between the numerator (2) and the denominator (19). The number 2 is a prime number, divisible only by 1 and 2. The number 19 is also a prime number, divisible only by 1 and 19. Since they share no common factors other than 1, the fraction 2/19 is already in its simplest form.

Therefore, the final answer is 2/19. Yay, another problem solved!

Key Points:

  • Common Denominators: Ensure the denominators are the same before subtracting.
  • Subtract Numerators: Subtract the top numbers.
  • Keep Denominator: The denominator stays the same.
  • Simplify: Check if the fraction can be simplified. In this case, 2/19 is already in its simplest form.

4. Subtracting Fractions: 9/13 - 3/13

Okay, guys, let's keep rolling with fraction subtraction! This time we have 9/13 - 3/13. As always, the first thing we're looking for is whether the denominators are the same. And yep, both fractions have a denominator of 13. That makes things much simpler for us!

With the denominators being the same, we can go ahead and subtract the numerators. We're subtracting 3 from 9:

9 - 3 = 6

Now, we pop that result over the original denominator, which is 13. So, our fraction is:

6/13

Before we box this one up, we've gotta check if we can simplify the fraction. To do that, we look for common factors between the numerator (6) and the denominator (13). The factors of 6 are 1, 2, 3, and 6. The number 13 is a prime number, so its only factors are 1 and 13. Since 6 and 13 don't share any common factors other than 1, the fraction 6/13 is already in its simplest form.

So, our final answer is 6/13. High five!

Key Points:

  • Common Denominators: Always verify the denominators are the same before subtracting.
  • Subtract the Numerators: Subtract the top numbers.
  • Keep the Denominator: The denominator stays the same.
  • Simplify the Fraction: Always check to see if the fraction can be simplified.

5. Subtracting Fractions: 47/100 - 44/100

Alright, let's tackle our last fraction subtraction problem: 47/100 - 44/100. As we've done with the other problems, the very first step is to check if the denominators are the same. Both fractions have a denominator of 100, so we're good to go!

Since the denominators are the same, we can subtract the numerators. We need to subtract 44 from 47:

47 - 44 = 3

Now, we put that result over the original denominator, which is 100. So, our answer is:

3/100

Before we declare our mission accomplished, we need to check if we can simplify this fraction. To simplify, we look for common factors between the numerator (3) and the denominator (100). The number 3 is a prime number, which means its only factors are 1 and 3. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Since 3 and 100 don't share any common factors other than 1, the fraction 3/100 is already in its simplest form.

So, our final answer is 3/100. We did it! Great job everyone!

Key Points:

  • Common Denominators: Make sure the denominators are the same.
  • Subtract the Numerators: Subtract the top numbers.
  • Keep the Denominator: The denominator stays the same.
  • Simplify the Fraction: Always check to see if the fraction can be simplified.

Hope this helps you nail fraction arithmetic! Keep practicing, and you'll become a fraction master in no time. You got this!