Subtracting Fractions with Unlike Denominators | Math with Mr. J
Summary
TLDRIn 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
📚 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.
🔍 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.
Mindmap
Keywords
💡Common Denominator
💡Least Common Multiple (LCM)
💡Renaming Fractions
💡Numerator
💡Denominator
💡Subtracting Fractions
💡Equivalent Fractions
💡Simplifying Fractions
💡Greatest Common Factor (GCF)
💡Multiples
💡Arithmetic Operations
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.
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