Subtracting Fractions with Unlike Denominators | Math with Mr. J

Summary

In this educational video, Mr. J teaches viewers how to subtract fractions with unlike denominators. He emphasizes the importance of finding a common denominator by identifying the least common multiple (LCM) of the denominators. The video demonstrates the process of renaming fractions to have equivalent denominators and then subtracting the numerators. Mr. J simplifies the resulting fractions, showcasing the method with examples, such as 5/6 - 3/12 and 9/10 - 2/4, leading to simplified answers of 7/12 and 2/5, respectively. He also provides additional resources for further understanding.

Takeaways

• 📘 Subtracting fractions with unlike denominators requires a common denominator, similar to addition.
• 🔍 Finding the least common multiple (LCM) of the denominators is crucial for determining the common denominator.
• 📋 Writing out multiples of each denominator is a practical method to find the LCM.
• 🔄 Renaming fractions involves adjusting both the numerator and the denominator to create an equivalent fraction with the common denominator.
• ➗ Subtracting the numerators of the renamed fractions with the common denominator gives the preliminary result.
• 🔍 After subtraction, always check if the resulting fraction can be simplified by finding the greatest common factor (GCF).
• 📝 The script provides a step-by-step guide to subtracting fractions, starting with finding a common denominator.
• 📖 Examples are used to illustrate the process, making it easier to understand the method.
• 🔗 Links to related videos for further clarification on topics like finding LCM and simplifying fractions are provided.
• 📚 The script is part of a series, with part two offering additional examples and insights.
• 👋 The presenter concludes with a friendly sign-off, encouraging viewers to seek further help if needed.

Q & A

What is the main topic covered in the Math with Mr. J. video?

The main topic covered in the video is how to subtract fractions with unlike denominators.

Why is it necessary to have a common denominator when subtracting fractions?

A common denominator is necessary to ensure that the fractions can be directly compared and subtracted without altering their values, as fractions with different denominators represent different parts of a whole.

What is the least common multiple and why is it used when finding a common denominator for fractions?

The least common multiple (LCM) is the smallest number that is a multiple of both denominators. It is used to find a common denominator because it simplifies the process and reduces the complexity of the fractions involved.

How can you find the least common multiple between two numbers?

You can find the LCM by writing out multiples of both numbers and identifying the smallest number that appears in both lists of multiples.

What is the first step when subtracting fractions with unlike denominators, according to the video?

The first step is to find a common denominator by identifying the least common multiple between the two denominators.

What is the process of renaming a fraction in the context of subtraction with unlike denominators?

Renaming a fraction involves adjusting both the numerator and the denominator so that the fraction is equivalent to its original value but has the common denominator identified for the subtraction.

In the example with 5/6 and 3/12, what is the least common multiple and how is it found?

The least common multiple for 5/6 and 3/12 is 12, which is found by listing multiples of 6 and noticing that 12 is a multiple of both 6 and 12.

How is the fraction 5/6 renamed to have a common denominator of 12?

The fraction 5/6 is renamed by multiplying both the numerator and the denominator by 2, resulting in the equivalent fraction 10/12.

What is the final simplified answer for the subtraction problem 5/6 - 3/12, and why is it in simplest form?

The final simplified answer is 7/12. It is in simplest form because 7 and 12 have no common factors other than 1.

In the second example with 9/10 and 2/4, what is the least common multiple and how is it determined?

The least common multiple for 9/10 and 2/4 is 20, determined by extending the list of multiples for both 10 and 4 until a common multiple is found.

How is the fraction 2/4 renamed to have a common denominator of 20?

The fraction 2/4 is renamed by multiplying both the numerator and the denominator by 5, resulting in the equivalent fraction 10/20.

What is the final simplified answer for the subtraction problem 9/10 - 2/4, and how is it simplified?

The final simplified answer is 2/5. It is simplified by dividing both the numerator and the denominator of 8/20 by their greatest common factor, which is 4.

Outlines

00:00

📚 Subtracting Fractions with Unlike Denominators

In this educational video, Mr. J introduces the concept of subtracting fractions with unlike denominators. He emphasizes the importance of finding a common denominator before proceeding with the subtraction, explaining that the least common multiple (LCM) is preferred for simplicity. The process of identifying the LCM by listing multiples of the denominators is demonstrated using the example of 5/6 minus 3/12. Mr. J shows how to rename the fractions with the common denominator of 12, perform the subtraction, and simplify the result to get 7/12, which is already in its simplest form.

05:02

🔍 Simplifying Fractions After Subtraction

Continuing the lesson, Mr. J tackles a second example, 9/10 minus 2/4, to illustrate the process of finding a common denominator when the LCM is not immediately obvious. He extends the list of multiples for both denominators until he identifies 20 as the LCM. Mr. J then renames both fractions with the common denominator of 20, performs the subtraction to get 8/20, and simplifies the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 4, resulting in the simplified answer of 2/5. The video also provides additional resources for further understanding of simplifying fractions and subtracting fractions with unlike denominators.

Keywords

💡Common Denominator

A common denominator is a shared denominator between two or more fractions, which is necessary for performing arithmetic operations like addition or subtraction. In the video, finding a common denominator is the first step in subtracting fractions with unlike denominators. For instance, when subtracting 5/6 from 3/12, the least common multiple of 6 and 12 is determined to be 12, making it the common denominator.

💡Least Common Multiple (LCM)

The least common multiple is the smallest number that is a multiple of two or more integers. In the context of the video, finding the LCM of the denominators is crucial to establish a common denominator for fractions. The script illustrates this by finding the LCM of 6 and 12, which is 12, thus allowing the fractions to be renamed with this common denominator.

💡Renaming Fractions

Renaming fractions involves converting fractions with different denominators into equivalent fractions with a common denominator. This process is demonstrated in the video when the fraction 5/6 is renamed to 10/12 to match the common denominator found. Renaming ensures that the value of the fractions remains the same while allowing for subtraction.

💡Numerator

The numerator is the top number in a fraction, representing the number of parts being considered. In the video, when renaming fractions, the numerators are adjusted to create equivalent fractions with the new common denominator. For example, the numerator of 5/6 is multiplied by 2 to become 10/12.

💡Denominator

The denominator is the bottom number in a fraction, indicating the total number of equal parts into which a whole is divided. The video emphasizes the importance of finding a common denominator for the denominators of the fractions involved in a subtraction operation.

💡Subtracting Fractions

Subtracting fractions is the process of taking one fraction away from another. The video script provides a step-by-step guide on how to subtract fractions with unlike denominators, starting with finding a common denominator and then proceeding to subtract the numerators while keeping the common denominator.

💡Equivalent Fractions

Equivalent fractions are fractions that have the same value even though they have different numerators and denominators. The concept is central to the video as it shows how to create equivalent fractions with a common denominator to perform subtraction. For example, 5/6 and 10/12 are equivalent fractions.

💡Simplifying Fractions

Simplifying fractions involves reducing fractions to their simplest form by dividing both the numerator and the denominator by their greatest common factor. The video mentions simplifying the final answer, 8/20, to 2/5 by dividing both by their greatest common factor, which is 4.

💡Greatest Common Factor (GCF)

The greatest common factor is the largest number that divides two or more numbers without leaving a remainder. In the video, the GCF is used to simplify fractions after subtraction. The GCF of 8 and 20 is found to be 4, which is used to simplify the fraction 8/20 to 2/5.

💡Multiples

Multiples are the result of multiplying a number by an integer. The video script uses the concept of multiples to find the least common multiple between two denominators. The multiples of 6 and 12 are listed to identify their LCM, which is essential for establishing a common denominator.

💡Arithmetic Operations

Arithmetic operations are mathematical procedures such as addition, subtraction, multiplication, and division. The video focuses on the subtraction operation, specifically with fractions that have unlike denominators, demonstrating how arithmetic operations are applied in the context of fractions.

Highlights

Introduction to the process of subtracting fractions with unlike denominators.

The necessity of a common denominator for subtraction, similar to addition.

Finding the least common multiple (LCM) between denominators to establish a common denominator.

The rationale for choosing the least common multiple for ease of calculation and simplification.

Method of listing multiples to identify the LCM when it's not immediately recognizable.

Demonstration of finding the LCM for the fractions 5/6 and 3/12, resulting in 12.

Renaming fractions to equivalent fractions with the common denominator.

Procedure to rename 5/6 to an equivalent fraction with a denominator of 12, resulting in 10/12.

Direct subtraction of the numerators once the fractions have been renamed with the common denominator.

Result of the first example is 7/12, which is already in simplest form.

Introduction to the second example involving fractions 9/10 and 2/4.

Finding the LCM for 10 and 4, which is 20, and renaming the fractions accordingly.

Renaming 9/10 to 18/20 and 2/4 to 10/20 using the common denominator.

Subtraction of the renamed fractions yielding 8/20.

Simplification of 8/20 to its simplest form, 2/5, using the greatest common factor.

Clarification that while 8/20 is correct, it can be simplified for a cleaner answer.

Offer of additional resources for further help with simplifying fractions.

Announcement of a follow-up video covering more examples of subtracting fractions with unlike denominators.

Transcripts

Welcome to Math with Mr. J.

In this video, I'm going to cover how to subtract fractions with unlike denominators.

So let's jump into our examples, starting with number one, where we have 5/6 minus

3/12. Now, when we subtract fractions, we need a common denominator just like when

we add fractions. For number one, we have a 6 and the 12, so we don't have a common

denominator to start with, so we can't subtract quite yet. The first thing that we

need to do is find a common denominator and we can do that by finding the least common

multiple between our denominators. We want the least because smaller numbers in value

are generally easier to work with and this will help cut down on simplifying in the

end once we get to our answer. As far as why we need a common denominator, that's

a topic for another video, I'll drop that link down in the description. Now, as you're

looking at a subtraction problem involving fractions with unlike denominators, you

may recognize the least common multiple between denominators right away, but if not,

you can always write out your lists of multiples in order to find it. So let's start

by writing some multiples of both 6 and 12 and see if we can find that least common

multiple. We'll start with 6, so I'm going to come to the bottom of the screen where

I have some extra room to write out these lists and we'll start with 6. So I would

suggest writing out four or five multiples for each denominator and see if you can

find that least common multiple. If not, you can always extend the lists until you

find that least common multiple. So if four or five multiples don't work and you

don't see any common multiples, extend those lists. So the first four multiples of 6 are 6,

12,

18, 24.

Now we'll do 12. So the first multiple of 12 is 12. Now, no need to go on if you find

that least common multiple because if you look, we have a least common multiple of

12. So we are ready to move to the next step, which is rename. So 12 is going to

be our common denominator. I'm going to come back up to the original problem underneath

and start to write the renamed fractions with that common denominator of 12. So underneath,

I'll start these fractions with that common denominator of 12. And now we're going

to rename, will start with 5/6. So we're going to rename that fraction with an equivalent

fraction with the denominator of 12. So we need to think, how do we get the denominator

of 6 to equal the denominator of 12. 6 times what equals 12? Well, we know that 6

times 2 equals 12. So whatever we do to the denominator, the bottom number, we have

to do to the numerator, the top number, in order to keep this fraction equivalent,

we don't want to change the value of the problem at all. So we need to do 5 times

2 to get the renamed numerator. 5 times 2

is 10, so 10/12 is equivalent to 5/6. So we renamed with that denominator of 12. Now

we need to do 3/12. Well, 3/12 already has a denominator of 12, so we don't need

to rename. We can just bring the 3 down. Once we rename, we can subtract. When we

subtract fractions, we subtract the numerators, so 10 minus 3 is 7, and then we keep

the denominator of 12 the same. So 7/12 is our answer. Now always look to simplify.

So can we simplify 7/12? Well, 7/12 is in simplest form, the only common factor between

7 and 12 is 1, so we can't break this down any further as far as simplifying goes.

So our final simplified answer, 7/12. Let's try another one and move on to number

two, where we have 9/10 minus 2/4. So the first thing that we need to do, find a

common denominator. So we need that least common multiple between 10 and 4. And that's

going to be our common denominator. Let's go down to the bottom and write out some

multiples. So we'll start with 10 and we'll write out four multiples to start with.

So 10, 20, 30, 40. Now let's write out four multiples of 4 and see if we have a least

common multiple. So 4, 8, 12, 16. So writing out four multiples for each, we don't

have a match, so we need to extend our lists. Now the multiples of 10, we are already

at 40 and the multiples of 4 were only at 16. So let's extend that one and the next

multiple of 4 is 20 and that's going to give us a common multiple and specifically,

the least common multiple. So we're going to use 20 for our common denominator. Let's

go back up to the original problem underneath and rename with that common denominator of 20.

We'll start with 9/10. So how do we get that denominator of 10 to equal 20? Well,

10 times 2 is 20. And whatever we do to the denominator, we have to do to the numerator

in order to keep this equivalent. So 9 times 2 gives us 18 for our renamed numerator.

So 18/20 is equivalent to 9/10. We just have that common denominator, 20 now. Now

we need to do 2/4. So how do we get 4 to equal 20? Well, we know 4 times 5 equals

20, so 4 times 5 equals 20. So we need to do the same thing to the numerator in order

to get that renamed equivalent fraction with the denominator of 20. So same thing

to the numerator. 2 times 5 gives us 10.

Now we're ready to subtract, so subtract the numerators, the top numbers. 18 minus 10 is 8.

Keep the denominator of 20 and our final answer is 8/20.

Now 8/20 can be simplified. There are multiple paths that we can take in order to

get this into simplest form, but if we use the greatest common factor between 8 and

20, we can simplify it in one step. The greatest common factor between 8 and 20 is

4, so let's divide both of these by 4 in order to get our simplified answer. So 8

divided by 4 and 20 divided by 4. That's going to give us a simplified answer of 2/5.

So 2/5 is our final simplified answer. Now, just to be clear, 8/20 is the correct

answer, but we were able to simplify that fraction and get a simplified answer of

2/5. If you need more help or clarification with simplifying fractions, I added a

link to my video about that down in the description. As far as subtracting fractions

with unlike denominators, this was part one. I do have a part two where I go through

two more examples. I'll add that link down in the description as well. I hope that

helped. Thanks so much for watching. Until next time. Peace.