Learn Fractions In 7 min ( Fast Review on How To Deal With Fractions)
Summary
TLDRThis video aims to provide a quick review of fractions, covering basic concepts like mixed numbers, improper fractions, and proper fractions. It teaches how to convert between these forms, simplify fractions, and perform arithmetic operations like addition, subtraction, multiplication, and division. The presenter also introduces a shortcut method for adding and subtracting fractions, making it accessible for those struggling with fractions.
Takeaways
- π This video aims to review basic fractions in seven minutes, covering mixed fractions, improper fractions, simplifying fractions, multiplication, division, addition, and subtraction.
- π’ Mixed fractions combine a whole number and a fraction, like 3 1/2, which can be converted to an improper fraction by multiplying the denominator with the whole number and adding the numerator (e.g., 3 1/2 = 7/2).
- βοΈ Improper fractions, where the numerator is larger than the denominator (e.g., 10/3), can be converted to mixed numbers by dividing the numerator by the denominator (e.g., 10/3 = 3 1/3).
- π Proper fractions have a numerator smaller than the denominator (e.g., 1/2).
- βοΈ Simplifying fractions involves reducing them to their simplest form by dividing both the numerator and denominator by their greatest common divisor (e.g., 10/24 simplifies to 5/12).
- βοΈ Multiplying fractions is straightforward: multiply the numerators and denominators respectively (e.g., 2/5 * 3/4 = 6/20, which simplifies to 3/10).
- β Dividing fractions involves flipping the second fraction (reciprocal) and then multiplying (e.g., 3/8 Γ· 6/10 becomes 3/8 * 10/6 = 30/48, which simplifies).
- ββ Adding and subtracting fractions can be simplified using the 'bowtie method': multiply diagonally for the numerators, and then multiply the denominators (e.g., 2/3 + 5/7 = (2*7 + 5*3) / (3*7) = 29/21).
- π The 'bowtie method' also applies to subtraction, following the same steps but using a subtraction operator (e.g., 3/8 - 1/4 = (3*4 - 1*8) / (8*4) = 20/32, which simplifies to 5/8).
- π Mixed number operations involve converting them to improper fractions first, then applying the appropriate operation (e.g., 3 1/2 Γ· 2 1/3 becomes 7/2 Γ· 7/3).
Q & A
What is the main goal of the video?
-The main goal of the video is to help viewers understand fractions within about seven minutes, providing a quick review of the basic concepts and common problems related to fractions.
What is a mixed fraction?
-A mixed fraction is a number that combines a whole number and a fraction, such as 3 1/2.
How can you convert a mixed fraction to an improper fraction?
-To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. For example, for 3 1/2, you would calculate 2*3 + 1 = 7, resulting in the improper fraction 7/2.
What defines an improper fraction?
-An improper fraction is a fraction where the numerator is larger than the denominator, such as 10/3.
How do you simplify a fraction?
-To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number. For example, to simplify 10/24, divide both by 2 to get 5/12.
What is the method for multiplying fractions?
-To multiply fractions, multiply the numerators together and the denominators together. For example, (2/5) * (3/4) = (2*3)/(5*4) = 6/20, which simplifies to 3/10.
How do you handle division of fractions?
-To divide fractions, invert (flip) the second fraction and then multiply. For example, (3/8) Γ· (5/6) becomes (3/8) * (6/5) = (3*6)/(8*5) = 18/40, which simplifies to 9/20.
What is the 'bowtie' method mentioned in the video?
-The 'bowtie' method is a technique for adding and subtracting fractions. It involves multiplying across the fractions in a crisscross pattern and then summing or subtracting the products, and finally multiplying the denominators for the new denominator.
Can you explain the 'bowtie' method with an example?
-For example, to add 2/5 and 3/7 using the 'bowtie' method, calculate (2*7) + (5*3) for the numerator and (5*7) for the denominator. This gives (14 + 15)/35 = 29/35.
How can mixed numbers be handled in operations like division?
-Mixed numbers can be converted into improper fractions before performing operations. For example, 3 1/2 Γ· 2 1/3 is converted to 7/2 Γ· 7/3, then solved by inverting the second fraction and multiplying, resulting in 21/14, which simplifies to 3/2.
Outlines
π Introduction and Objective of the Video
The goal of this video is to provide a quick review of fractions in seven minutes. It is intended for viewers who have some prior knowledge of fractions. The video will cover common fraction problems, including converting mixed fractions to improper fractions, simplifying fractions, and basic fraction operations.
π’ Converting Mixed Fractions to Improper Fractions
A mixed fraction consists of a whole number and a fraction. To convert it to an improper fraction, multiply the denominator by the whole number and add the numerator. The result is placed over the original denominator. Example: 3 1/2 becomes 7/2.
β Converting Improper Fractions to Mixed Numbers
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number part, and the remainder is the numerator of the fractional part. Example: 10/3 becomes 3 1/3.
β Simplifying Fractions
Simplifying fractions involves reducing them to their simplest form. This is done by dividing both the numerator and the denominator by their greatest common factor. Example: 10/24 simplifies to 5/12. Another method involves canceling common factors in the numerator and denominator.
βοΈ Multiplying Fractions
Multiplying fractions is straightforward: multiply the numerators together and the denominators together. Simplify the result if possible. Example: 2/5 * 3/4 becomes 6/20, which simplifies to 3/10.
β Dividing Fractions
To divide fractions, multiply the first fraction by the reciprocal (inverse) of the second fraction. Example: 3/8 Γ· 6/10 becomes 3/8 * 10/6, which simplifies to 30/48 and further to 5/8.
β Adding and Subtracting Fractions Using the Bowtie Method
The Bowtie Method is a quick way to add and subtract fractions without finding the lowest common denominator. Multiply the denominators for the common denominator. Cross-multiply the numerators, add or subtract them, and place the result over the common denominator. Simplify the final fraction. Example: 2/3 + 5/7 becomes (2*7 + 3*5)/(3*7) = 29/21.
π Simplifying Results from the Bowtie Method
When using the Bowtie Method, the resulting fraction might not be in its simplest form. Ensure to simplify it by finding common factors. This method is particularly useful for complex algebraic fractions.
β Subtracting Fractions with the Bowtie Method
The same Bowtie Method applies to subtraction. Multiply diagonally, subtract the products, and place the result over the product of the denominators. Example: 8/3 - 1/4 becomes (8*4 - 3*1)/(3*4) = 29/12.
π Working with Mixed Numbers in Operations
Convert mixed numbers to improper fractions before performing operations like addition, subtraction, multiplication, and division. After solving, convert the result back to a mixed number if necessary.
π Conclusion and Encouragement
The video wraps up by encouraging viewers to practice the methods shown. The creator hopes the video aids in understanding fractions better and invites viewers to subscribe and give feedback.
Mindmap
Keywords
π‘Fractions
π‘Mixed Fraction
π‘Improper Fraction
π‘Numerator
π‘Denominator
π‘Proper Fraction
π‘Simplifying Fractions
π‘Multiplying Fractions
π‘Dividing Fractions
π‘Bowtie Method
Highlights
The goal of the video is to understand fractions in about seven minutes.
The video is a quick review of basic functions dealing with fractions.
Mixed fractions are numbers with a whole number and a fraction, e.g., 3 and 1/2.
To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator.
Improper fractions are fractions where the numerator is greater than the denominator.
Proper fractions have a numerator smaller than the denominator, like 1/2.
Mixed numbers are written with a whole number and a proper fraction.
To convert an improper fraction to a mixed number, divide the numerator by the denominator.
Fractions should always be simplified or reduced to their simplest form.
To simplify a fraction, find a common factor for both the numerator and the denominator and cancel them out.
Multiplying fractions involves multiplying the numerators together and the denominators together.
Division of fractions is converted into multiplication by multiplying by the reciprocal of the second fraction.
The Bowtie method is a shortcut for adding and subtracting fractions without finding the lowest common denominator.
In the Bowtie method, multiply the numerators and denominators across in a diagonal fashion.
Always simplify the final answer in fraction operations.
Convert mixed numbers to improper fractions before performing operations like division.
The video is a crash course aimed at helping those struggling with basic fraction operations.
The video concludes with a reminder to simplify answers and a prompt to subscribe for more math content.
Transcripts
okay so the goal of this video is to get
you to understand fractions in about
seven minutes so let's see if we can do
it really obviously I am I going to get
you to completely master fractions in
seven minutes
no I'm expecting that you've studied
fractions before so this is going to be
like just a quick review of the basic
functions with dealing of fractions but
we are going to cover pretty much the
whole scope of most common problems that
you have when you're working with
fractions okay so I've got seven
problems let's start with the first one
all right so 3 and 1/2 this is called a
mixed fraction okay so if you have a
number and a little fraction next to it
that's called a mixed fraction so we
need to be able to write a mixed
fraction as an improper fraction that's
a fraction like down here like 10 over 3
so the way you do that is just you take
this bottom number two and you multiply
it by three and then we're going to add
the one so you probably remember how to
do that so that's gonna be 2 times 3
that's 6 plus 1 is gonna be 6 plus 1
that's 7 over 2 okay so we need to be
able to take mixed number fractions and
turn them into improper fractions now we
also need to let's move on our second
problem take improper fractions and
write them as a mixed number so that
what we do there is we simply go ahead
and just divide so this is 10 divided by
3 so we've got a 3 or a 10 divided by 3
right this way
so 3 goes into 10 three times 3 times 3
is 9 we have 1 as a remainder so we're
gonna write with this remainder is 1 1
and then whatever number this is just 3
is we're gonna write it just like this
so that's 3 and 1/3 so 10 thirds okay is
equal to 3 and 1/3 so just basic
fraction terminology this is an improper
fraction because the numerator matter
fact I should just got to break this up
here 10 over 3 when we're dealing with
fractions the top number is the
numerator the bottom number is the
denominator okay so
the numerator number is bigger than the
denominator number we call that an
improper fraction now I talked about
mixed numbers okay so I can write this
as 3 and 1/2 so this is a mixed number
this is an improper fraction and a
proper fraction is where the numerator
is less than the denominator so
something like 1/2 okay so the
denominator down here is bigger than the
numerator so this is a proper fraction
improper fraction and mixed numbers so
you need to kind of be able to go back
and forth between the two ok so we're on
the number three and let's see here so
in this one I wanted to talk about very
quickly the idea of reducing or
simplifying a fraction so here I have 10
over 24 when you're dealing with
fractions you always want to reduce them
or write them in their simplest form so
the idea here is to think of a number
that goes into both 10 and 24 so you
might have thought to yourself well it's
two okay and that's good so 2 goes into
10 how many times five times and 2 goes
into 24 12 times ok so this fraction
1024 is equivalent to the simpler
fraction five twelfths now another way
you can think about reducing or
simplifying fractions and we're going to
write this over here 1024 is to look at
the factors of these numbers in other
words 10 is the same thing as 2 times 5
and 24 is the same thing as 2 times 12
so anytime you have that and these are
called factors again okay now where the
this 10 can be written as a product of
these numbers these are the factors of
this number here but anytime you have
the same factor in both the numerator
and denominator we could do something
called cross cancel essentially just get
rid of them and then whatever is left is
the answer okay this is more the
simplified fraction so 1024 is
equivalent to the fraction 512 okay so
we talked about the basic part so far
our fractions numerator denominator
proper fraction improper fraction mixed
number and now simplifying so remember
when you're dealing with fractions you
always want to work with fractions in
our simplest forms or your final answer
you want to reduce okay all right let's
move on to number four okay so hopefully
I can get the Sun in seven minutes I may
go over a little bit but just think
you'll you'll understand fractions here
crash course alright so now we have two
fractions here doesn't make a difference
if they're improper proper okay but the
idea is we want to multiply them so I
have one fraction and I want to multiply
it by another fraction this is very easy
okay
all you need to do is simply multiply
the respective numerators and
denominators so two times three is six
five times four is twenty okay and then
here this is a valid correct answer
however you always want to simplify your
answers reduce it
okay this was kind of brings us back to
the previous problem so you can think of
six as what two times three is I just
wrote this in twenty I can think of well
I think it's five times four but I can
also think of as two times ten okay so
I'm looking to create kind of common
factor so I could cross cancel and I'm
left with the fraction 3/10 okay so 3/10
is the simplified version of 6 xx
mathematically they're equivalent okay
but you always want to leave your final
answers fully reduced or simplified okay
so we got multiplication down let's talk
about division so division is actually
quite easy as well what we do with
fractions is we don't actually divide
fractions we're going to turn this
problem into a multiplication problem
and because the previous problem here I
showed you how to multiply so we only
know how to do that I'm gonna we're
going to turn this into a multiplication
problem then we're going to do what we
did in pron them before so what we do
there it's very easy is we write the
first fraction again that's 3
8.now we're gonna change the division
sign here into multiplication now here's
the deal in order to change this from
division to multiplication you have to
take this fraction to the right of the
symbol the division symbol and flip it
upside down it's called the reciprocal
or inverse just flip it upside down so
that's gonna be 10 over 6 okay so now I
have a multiplication problems I'm going
to do what I did in prom before ok I'm
simply going to multiply the respective
numerators and denominators so 3 times
10 is 30 and 6 times a 8 times 6 excuse
me is 48 and then I would go ahead and
simplify okay I'm actually going to skip
that right now because I want to try to
see if I can finish this video up in a
pretty timely manner however we would
want to simplify as I showed you in
prams 3 and 4 okay but technically
speaking all right this is a correct
answer now let's kind of stop and pause
if you think about the operations that
we do with numbers ok infractions are
nothing more than numbers we multiply we
divide we add and we subtract so as I
showed you with fractions multiplication
and division are effectively the same
step we have to take an extra step with
division but we end up just multiplying
the same thing is going to be true with
addition and subtraction effectively
you're going to do the same things now
for the purposes of this video because
I'm one a Lumpkin I'm directing this
video towards somebody who is like maybe
totally forgot fractions or really
struggling but I'm gonna teach you a way
to add and subtract fractions that we're
gonna bypass what they kind of teach you
in school as far as the lowest common
denominator and all that kind of good
stuff so I'm gonna give you a shortcut
method the idea here is that I'm just
giving you a procedure to use that
you'll get these problems right every
time
ok so let's talk about addition and
subtraction procedure is the same okay
no matter what whether whether you're
dealing with adding or subtracting so
here it goes it's called the bo time
so the way it works is this you start
with this number down here okay so it's
the fraction to the right okay actually
doesn't have to be in this particular
order but this is the way I do it I
would suggest you do it my way and just
remember the this procedure is three
steps and you'll be done so it's going
to be this number of times this number
so let's go ahead and write that here so
five times two is what ten we'll write
that there this is an addition problem
so I'm going to write a plus then you're
going to take this number and we're
going to multiply across this way okay
in a diagonal fashion so 3 times 7 is 21
okay
this is our numerator so we're gonna
draw a little fraction bar now to get to
our denominator we just simply multiply
the bottom numbers okay so 3 times 5 is
15 and we just simplify this 10 times 21
is 31 over 15 and you're done that is it
so this is a great method because when
you're dealing with algebra by the way
we just say one other thing here you
would want to simplify this answer so if
you got an answer let's say 30 over 48
or something you want to simplify the
answer the disadvantage for using this
method for all proms is that sometimes
you won't be you'll you'll get a
fraction it doesn't have the lowest
common denominator so technically you
still need to understand that if you're
in a algebra course or whatnot but doing
it by adding fractions this way you'll
get them right every single time
and by the way let's just take a look at
a quick algebra problem let's say I have
something like this so you may not
understand this completely but if I want
it to add these fractions I go x times X
I'm following the same step x times X
happens to be x squared okay
y times Z sorry this is addition
problems so it's going to plus y times Z
is why Z over Y times X and that's it
this is a great method I refer to it as
a bowtie method
so you definitely want to learn this or
keep this in your kind of like back
pocket okay so if you forget anything
about fractions you can always do this
for addition and subtraction okay let's
do this last problem here we're using
the exact same method starting with this
bottom number we're gonna go this way
eight times three is what 24 now because
this is a subtraction problem we need we
need to use the subtraction operator so
that's gonna be four times one we're
doing the exact same steps as a previous
problem is four over that's our
numerator of four times eight which is
what 32 so our answer is going to be 20
over 32 and of course we can reduce this
okay 20 is the same thing as 4 times 5
and 32 is the same thing as 4 times 8 so
I have these common factors which I can
cross cancel and I'm left with my final
answer whoops and about them I don't
live with my final answer five-eighths
okay and that is it okay so really
fractions I'm not sure how long this
video is gone but you pretty much
learned a month's worth of fractions
crash course hopefully I was I'm sure
I'm over seven minutes but who cares the
deal is that you know what you probably
like remember all the stuff that you had
to go through now there is obviously a
few other things that you need to know
with fractions and just make one other
comment here let's suppose you had a
problem like 3 and 1/2 divided by 2 and
one thirds okay so you're like well how
do I deal with that you know I don't see
how I you know whether this is adding
subtracting multiplying dividing the
deal is with these mixed numbers just
convert them into improper fractions so
3 and 1/2 is the same thing as what's 3
times 2 is 6 plus 1 7 halves divided by
this is going to be 6 plus now this is
actually the same thing right so 6
is seven-halves okay so you would just
this is a just kind of worked out way I
just picked these random numbers but you
get the idea this is the same thing as
that this is the same thing as that and
then you would do this problem using the
steps I just showed you
okay so finish this video up I hope that
you find this video useful and you
subscribe to my channel I do a ton of
math science stuff mostly kind of math
so my backgrounds of math math math
teacher but I'm trying to help out those
of your like are really struggling and
you just need some kind of basic crash
course just to do problems and when it
comes to fractions this is certainly
helpful and if you like this video
please give it a thumbs up and let me
know how it goes let me know if this is
actually helping you so good luck with
you good luck with your fractions and
hope to see you soon
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