Mastering Fraction Subtraction A Step-by-Step Guide

Hey guys! Let's dive into some fraction subtraction problems. We're going to break down each one step-by-step so you can master this skill. Fraction subtraction might seem a bit tricky at first, but trust me, once you get the hang of finding common denominators, it becomes super easy. We'll go through several examples together, ensuring you understand not just the how but also the why behind each step. So, grab your pencils, and let's get started!

(a) Subtracting Fractions: 5/6 - 1/3

When we're tackling fraction subtraction, the golden rule is that we need a common denominator. Think of it like this: you can't subtract apples from oranges, right? Similarly, you can't directly subtract fractions with different denominators. So, in this case, we have 5/6 and 1/3. Our denominators are 6 and 3. To find a common denominator, we need to find the least common multiple (LCM) of 6 and 3. What's the smallest number that both 6 and 3 divide into evenly? Yep, it's 6!

Now, let's convert the fractions. The first fraction, 5/6, already has the denominator we want, so we can leave it as is. But the second fraction, 1/3, needs some adjusting. We need to multiply both the numerator (the top number) and the denominator (the bottom number) by the same number so that the denominator becomes 6. What do we multiply 3 by to get 6? That's right, 2! So, we multiply both the numerator and the denominator of 1/3 by 2:

(1 * 2) / (3 * 2) = 2/6

Now we have our equivalent fractions: 5/6 and 2/6. Great! Now we can actually subtract! All we need to do is subtract the numerators (5 - 2) and keep the denominator the same. So:

5/6 - 2/6 = (5 - 2) / 6 = 3/6

We're not quite done yet! Always remember to simplify your fractions to their lowest terms. Can we simplify 3/6? Absolutely! Both 3 and 6 are divisible by 3. So, let's divide both the numerator and the denominator by 3:

(3 ÷ 3) / (6 ÷ 3) = 1/2

So, the final answer for 5/6 - 1/3 is 1/2. See? Not so scary when you break it down step by step.

(b) Subtracting Fractions: 4/5 - 3/10

Alright, let's move on to the next problem: 4/5 - 3/10. Just like before, the first thing we need to do is find a common denominator. We have the denominators 5 and 10. What's the least common multiple of 5 and 10? If you said 10, you're spot on! 10 is the smallest number that both 5 and 10 divide into evenly.

Now, let's convert our fractions. The fraction 3/10 already has the denominator we want, so we can leave it as it is. But the fraction 4/5 needs to be converted. We need to multiply both the numerator and the denominator of 4/5 by the same number to get a denominator of 10. What do we multiply 5 by to get 10? You guessed it, 2! So, let's multiply:

(4 * 2) / (5 * 2) = 8/10

Now we have our equivalent fractions: 8/10 and 3/10. Fantastic! We're ready to subtract. Subtract the numerators (8 - 3) and keep the denominator the same:

8/10 - 3/10 = (8 - 3) / 10 = 5/10

Time to simplify! Can we simplify 5/10? You bet we can! Both 5 and 10 are divisible by 5. So, let's divide both the numerator and the denominator by 5:

(5 ÷ 5) / (10 ÷ 5) = 1/2

So, 4/5 - 3/10 equals 1/2. You're getting the hang of this!

(c) Subtracting Fractions: 7/9 - 2/3

Next up, we have 7/9 - 2/3. You know the drill by now, right? The first thing we need to identify is the common denominator. Our denominators are 9 and 3. What's the least common multiple of 9 and 3? It's 9! 9 is the smallest number that both 9 and 3 divide into evenly.

The fraction 7/9 already has our desired denominator, so we can leave it as is. Now we need to convert 2/3. We need to multiply both the numerator and the denominator by the same number to get a denominator of 9. What do we multiply 3 by to get 9? That’s right, 3! Let's multiply:

(2 * 3) / (3 * 3) = 6/9

Now we have our equivalent fractions: 7/9 and 6/9. Perfect! Time to subtract those numerators and keep the denominator the same:

7/9 - 6/9 = (7 - 6) / 9 = 1/9

Now, can we simplify 1/9? Nope! It's already in its simplest form. So, the answer for 7/9 - 2/3 is 1/9. Awesome work!

(d) Subtracting Fractions: 7/12 - 1/3

Let's keep the ball rolling with 7/12 - 1/3. You're becoming pros at this! What’s the first step? You guessed it – finding the common denominator. We have 12 and 3 as our denominators. What’s the least common multiple of 12 and 3? It’s 12!

The fraction 7/12 is already good to go with a denominator of 12. So, we just need to convert 1/3. We need to multiply both the numerator and the denominator by the same number to get a denominator of 12. What do we multiply 3 by to get 12? That’s 4! Let's do the math:

(1 * 4) / (3 * 4) = 4/12

Now we have our equivalent fractions: 7/12 and 4/12. Excellent! Let’s subtract those numerators and keep the denominator the same:

7/12 - 4/12 = (7 - 4) / 12 = 3/12

Time to simplify! Can we simplify 3/12? Yes, we can! Both 3 and 12 are divisible by 3. Let's divide them:

(3 ÷ 3) / (12 ÷ 3) = 1/4

So, 7/12 - 1/3 equals 1/4. You’re doing such a great job!

(e) Subtracting Fractions: 11/12 - 5/6

We’re almost there! Let's tackle 11/12 - 5/6. You know the routine: find that common denominator! We have 12 and 6 as our denominators. What's the least common multiple of 12 and 6? It's 12!

The fraction 11/12 is ready to roll with the denominator of 12. Now, we need to convert 5/6. We need to multiply both the numerator and the denominator by the same number to get a denominator of 12. What do we multiply 6 by to get 12? That’s 2! Let's multiply:

(5 * 2) / (6 * 2) = 10/12

Now we have our equivalent fractions: 11/12 and 10/12. Fantastic! Let's subtract those numerators and keep the denominator the same:

11/12 - 10/12 = (11 - 10) / 12 = 1/12

Can we simplify 1/12? Nope, it's already in its simplest form! So, the answer to 11/12 - 5/6 is 1/12. You're nailing this!

(f) Subtracting Fractions: 5/8 - 1/2

Last but not least, let's finish strong with 5/8 - 1/2. Let's find that common denominator! Our denominators are 8 and 2. What's the least common multiple of 8 and 2? It's 8!

The fraction 5/8 already has our desired denominator. So, let’s convert 1/2. We need to multiply both the numerator and the denominator by the same number to get a denominator of 8. What do we multiply 2 by to get 8? That's 4! So, let's multiply:

(1 * 4) / (2 * 4) = 4/8

Now we have our equivalent fractions: 5/8 and 4/8. Awesome! Let’s subtract those numerators and keep the denominator the same:

5/8 - 4/8 = (5 - 4) / 8 = 1/8

Can we simplify 1/8? Nope, it's already as simple as it gets! So, the answer for 5/8 - 1/2 is 1/8. High five! You did it!

Final Thoughts on Fraction Subtraction

Wow, guys, you've worked through quite a few fraction subtraction problems! Remember, the key to subtracting fractions is finding that common denominator, converting your fractions, subtracting the numerators, and simplifying your answer. It might seem like a lot of steps at first, but with practice, it becomes second nature. Keep up the great work, and you'll be a fraction subtraction master in no time!