Adding And Subtracting Fractions With Simplest Form Examples

Hey guys! Let's dive into the world of fractions and tackle some addition and subtraction problems. We're going to focus on finding the sum or difference of fractions and making sure our answers are in the simplest form. So, grab your pencils, and let's get started!

Adding Fractions with Common Denominators

When adding fractions, the most crucial thing is to ensure they have a common denominator. If they do, the process becomes super straightforward. You simply add the numerators (the top numbers) and keep the denominator (the bottom number) the same. Once you've done that, double-check if you can simplify the resulting fraction. Simplifying means reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor (GCF). It’s like giving your fraction a makeover to make it look its best!

Let's look at the first problem: $\frac{7}{12} + \frac{11}{12}$. Notice that both fractions already have a common denominator, which is 12. This makes our job a whole lot easier. We can go straight ahead and add the numerators: 7 + 11 = 18. So, we now have $\frac{18}{12}$. But hold on, we're not quite done yet! We need to simplify this fraction.

To simplify, we need to find the GCF of 18 and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The greatest factor they have in common is 6. So, we divide both the numerator and the denominator by 6: $\frac{18 \div 6}{12 \div 6} = \frac{3}{2}$. Now, $\frac{3}{2}$ is an improper fraction (the numerator is greater than the denominator), which means we can convert it to a mixed number. To do this, we divide 3 by 2. We get 1 with a remainder of 1. So, $\frac{3}{2}$ is equal to $1 \frac{1}{2}$. Ta-da! We've added the fractions and simplified the result.

Subtracting Fractions with Common Denominators

Subtracting fractions is very similar to adding them. Again, the key is to make sure the fractions have a common denominator. If they do, you subtract the numerators and keep the denominator the same. And just like with addition, simplification is the final step to ensure your answer is in its simplest form. Think of it as the cherry on top of your fraction sundae!

Let's tackle the second problem: $\frac{20}{21} - \frac{2}{21}$. We see that both fractions have a common denominator of 21. Awesome! We can subtract the numerators: 20 - 2 = 18. This gives us $\frac{18}{21}$. Now, let's simplify. We need to find the GCF of 18 and 21. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 21 are 1, 3, 7, and 21. The GCF is 3. So, we divide both the numerator and the denominator by 3: $\frac{18 \div 3}{21 \div 3} = \frac{6}{7}$. And there you have it! $\frac{6}{7}$ is our simplified answer.

More Practice with Addition

Let's keep the ball rolling with another addition problem: $\frac{5}{8} + \frac{7}{8}$. We've got a common denominator of 8, which is fantastic news. We add the numerators: 5 + 7 = 12. This gives us $\frac{12}{8}$. Time to simplify! The GCF of 12 and 8 is 4. Dividing both the numerator and the denominator by 4, we get $\frac{12 \div 4}{8 \div 4} = \frac{3}{2}$. Just like before, we have an improper fraction. Converting it to a mixed number, we divide 3 by 2, which gives us 1 with a remainder of 1. So, $\frac{3}{2}$ is equal to $1 \frac{1}{2}$. We're becoming fraction pros, guys!

More Practice with Subtraction

Now, let's subtract some more: $\frac{17}{30} - \frac{7}{30}$. Common denominator? Check! It's 30. Subtract the numerators: 17 - 7 = 10. We get $\frac{10}{30}$. Simplifying time! The GCF of 10 and 30 is 10. Divide both by 10: $\frac{10 \div 10}{30 \div 10} = \frac{1}{3}$. Perfect! Our answer in simplest form is $\frac{1}{3}$. You guys are doing great!

Adding Mixed Numbers

Things get a little more interesting when we add mixed numbers (numbers with a whole number part and a fractional part). There are a couple of ways we can approach this. One method is to convert the mixed numbers into improper fractions and then add them as we did before. The other method is to add the whole number parts and the fractional parts separately, and then combine the results. Let's try both!

Let's take the problem $4 \frac{4}{5} + 3 \frac{2}{5}$. First, let's convert these mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator. This becomes our new numerator, and we keep the same denominator.

For $4 \frac{4}{5}$, we do (4 * 5) + 4 = 24. So, $4 \frac{4}{5}$ is equal to $\frac{24}{5}$.

For $3 \frac{2}{5}$, we do (3 * 5) + 2 = 17. So, $3 \frac{2}{5}$ is equal to $\frac{17}{5}$.

Now we add the improper fractions: $\frac{24}{5} + \frac{17}{5}$. We have a common denominator, so we add the numerators: 24 + 17 = 41. This gives us $\frac{41}{5}$.

Now we convert this back to a mixed number. We divide 41 by 5, which gives us 8 with a remainder of 1. So, $\frac{41}{5}$ is equal to $8 \frac{1}{5}$.

Let's try the other method: adding the whole number parts and fractional parts separately. We have $4 \frac{4}{5} + 3 \frac{2}{5}$.

Add the whole numbers: 4 + 3 = 7.

Add the fractions: $\frac{4}{5} + \frac{2}{5} = \frac{6}{5}$.

So we have 7 + $\frac{6}{5}$. Now, $\frac{6}{5}$ is an improper fraction. We convert it to a mixed number: 1 $\frac{1}{5}$.

Finally, we add the whole numbers: 7 + 1 = 8. So, our answer is $8 \frac{1}{5}$. Both methods give us the same result!

Adding Mixed Numbers - Another Example

Let's solidify our understanding with one more mixed number addition problem: $5 \frac{11}{15} + 3$. In this case, we're adding a mixed number to a whole number. This is actually quite straightforward. We simply add the whole numbers together and keep the fractional part the same.

So, we have $5 \frac{11}{15} + 3$. Add the whole numbers: 5 + 3 = 8. The fractional part remains $\frac{11}{15}$. So, our answer is $8 \frac{11}{15}$.

And that’s it, guys! We’ve covered adding and subtracting fractions with common denominators, simplifying fractions, and adding mixed numbers. Keep practicing, and you’ll become fraction masters in no time!

Remember, the key takeaways are:

• Make sure fractions have a common denominator before adding or subtracting.
• Simplify your answers to their lowest terms.
• When adding mixed numbers, you can convert them to improper fractions or add the whole number and fractional parts separately.

Keep up the great work, and happy fraction-ing!