Learn Fractions In 7 min ( Fast Review on How To Deal With Fractions)

Summary

This 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

• 📚 This video aims to review basic fractions in seven minutes, covering mixed fractions, improper fractions, simplifying fractions, multiplication, division, addition, and subtraction.
• 🔢 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).
• ↔️ 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).
• 📈 Proper fractions have a numerator smaller than the denominator (e.g., 1/2).
• ✂️ 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).
• ✖️ Multiplying fractions is straightforward: multiply the numerators and denominators respectively (e.g., 2/5 * 3/4 = 6/20, which simplifies to 3/10).
• ➗ Dividing fractions involves flipping the second fraction (reciprocal) and then multiplying (e.g., 3/8 ÷ 6/10 becomes 3/8 * 10/6 = 30/48, which simplifies).
• ➕➖ 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).
• 🔄 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).
• 🔄 Mixed number operations involve converting them to improper fractions first, then applying the appropriate operation (e.g., 3 1/2 ÷ 2 1/3 becomes 7/2 ÷ 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) ÷ (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 ÷ 2 1/3 is converted to 7/2 ÷ 7/3, then solved by inverting the second fraction and multiplying, resulting in 21/14, which simplifies to 3/2.

Outlines

00:00

🎓 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.

05:00

🔢 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.

10:01

➗ 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.

✅ 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.

✖️ 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.

➗ Dividing Fractions

To divide fractions, multiply the first fraction by the reciprocal (inverse) of the second fraction. Example: 3/8 ÷ 6/10 becomes 3/8 * 10/6, which simplifies to 30/48 and further to 5/8.

➕ 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.

📐 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.

➖ 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.

🔄 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.

👍 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.

Keywords

💡Fractions

Fractions represent parts of a whole and are composed of a numerator and a denominator. In the video, the speaker covers the basics of fractions, including mixed fractions, improper fractions, and simplifying fractions.

💡Mixed Fraction

A mixed fraction combines a whole number and a fraction, such as 3 and 1/2. The video explains how to convert mixed fractions to improper fractions by multiplying the denominator with the whole number and adding the numerator.

💡Improper Fraction

An improper fraction has a numerator larger than the denominator, like 10/3. The video demonstrates converting improper fractions to mixed fractions by dividing the numerator by the denominator.

💡Numerator

The numerator is the top part of a fraction, representing how many parts of the whole are being considered. For example, in the fraction 3/4, 3 is the numerator. The video highlights its role in identifying and working with fractions.

💡Denominator

The denominator is the bottom part of a fraction, indicating the total number of equal parts in the whole. In the fraction 3/4, 4 is the denominator. The video emphasizes understanding the denominator when converting and simplifying fractions.

💡Proper Fraction

A proper fraction has a numerator smaller than the denominator, such as 1/2. The video covers identifying proper fractions and distinguishes them from improper fractions and mixed numbers.

💡Simplifying Fractions

Simplifying or reducing fractions involves dividing the numerator and denominator by their greatest common divisor. The video explains the process and the importance of working with fractions in their simplest forms, such as reducing 10/24 to 5/12.

💡Multiplying Fractions

Multiplying fractions involves multiplying the numerators together and the denominators together. For example, 2/5 * 3/4 = 6/20. The video discusses the method and the importance of simplifying the result.

💡Dividing Fractions

Dividing fractions requires multiplying by the reciprocal of the second fraction. For instance, 3/8 ÷ 6/10 is changed to 3/8 * 10/6. The video details this method and shows how to perform the multiplication and simplify the result.

💡Bowtie Method

The bowtie method is a technique for adding and subtracting fractions by cross-multiplying and then simplifying. The video introduces this method as a shortcut for dealing with fractions without finding a common denominator.

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