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

TabletClass Math
31 May 201814:12

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

  • πŸ“š This video aims to review basic fractions in seven minutes, covering mixed fractions, improper fractions, simplifying fractions, multiplication, division, addition, and subtraction.
  • πŸ”’ 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).
  • πŸ“ˆ Proper fractions have a numerator smaller than the denominator (e.g., 1/2).
  • βœ‚οΈ 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).
  • βœ–οΈ Multiplying fractions is straightforward: multiply the numerators and denominators respectively (e.g., 2/5 * 3/4 = 6/20, which simplifies to 3/10).
  • βž— 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).
  • βž•βž– 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).
  • πŸ”„ 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).
  • πŸ”„ 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

00:00

πŸŽ“ 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

πŸ”’ 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

βž— 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.

βœ… 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.

βœ–οΈ 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.

βž— 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.

βž• 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.

πŸ“ 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.

βž– 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.

πŸ”„ 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.

πŸ‘ 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

πŸ’‘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.

πŸ’‘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.

πŸ’‘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.

πŸ’‘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.

πŸ’‘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.

πŸ’‘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.

πŸ’‘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.

πŸ’‘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.

πŸ’‘Dividing Fractions

Dividing fractions requires multiplying by the reciprocal of the second fraction. For instance, 3/8 Γ· 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.

πŸ’‘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

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okay so the goal of this video is to get

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you to understand fractions in about

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seven minutes so let's see if we can do

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it really obviously I am I going to get

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you to completely master fractions in

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seven minutes

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no I'm expecting that you've studied

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fractions before so this is going to be

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like just a quick review of the basic

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functions with dealing of fractions but

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we are going to cover pretty much the

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whole scope of most common problems that

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you have when you're working with

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fractions okay so I've got seven

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problems let's start with the first one

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all right so 3 and 1/2 this is called a

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mixed fraction okay so if you have a

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number and a little fraction next to it

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that's called a mixed fraction so we

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need to be able to write a mixed

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fraction as an improper fraction that's

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a fraction like down here like 10 over 3

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so the way you do that is just you take

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this bottom number two and you multiply

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it by three and then we're going to add

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the one so you probably remember how to

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do that so that's gonna be 2 times 3

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that's 6 plus 1 is gonna be 6 plus 1

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that's 7 over 2 okay so we need to be

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able to take mixed number fractions and

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turn them into improper fractions now we

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also need to let's move on our second

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problem take improper fractions and

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write them as a mixed number so that

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what we do there is we simply go ahead

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and just divide so this is 10 divided by

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3 so we've got a 3 or a 10 divided by 3

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right this way

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so 3 goes into 10 three times 3 times 3

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is 9 we have 1 as a remainder so we're

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gonna write with this remainder is 1 1

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and then whatever number this is just 3

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is we're gonna write it just like this

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so that's 3 and 1/3 so 10 thirds okay is

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equal to 3 and 1/3 so just basic

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fraction terminology this is an improper

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fraction because the numerator matter

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fact I should just got to break this up

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here 10 over 3 when we're dealing with

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fractions the top number is the

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numerator the bottom number is the

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denominator okay so

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the numerator number is bigger than the

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denominator number we call that an

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improper fraction now I talked about

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mixed numbers okay so I can write this

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as 3 and 1/2 so this is a mixed number

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this is an improper fraction and a

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proper fraction is where the numerator

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is less than the denominator so

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something like 1/2 okay so the

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denominator down here is bigger than the

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numerator so this is a proper fraction

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improper fraction and mixed numbers so

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you need to kind of be able to go back

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and forth between the two ok so we're on

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the number three and let's see here so

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in this one I wanted to talk about very

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quickly the idea of reducing or

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simplifying a fraction so here I have 10

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over 24 when you're dealing with

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fractions you always want to reduce them

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or write them in their simplest form so

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the idea here is to think of a number

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that goes into both 10 and 24 so you

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might have thought to yourself well it's

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two okay and that's good so 2 goes into

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10 how many times five times and 2 goes

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into 24 12 times ok so this fraction

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1024 is equivalent to the simpler

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fraction five twelfths now another way

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you can think about reducing or

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simplifying fractions and we're going to

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write this over here 1024 is to look at

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the factors of these numbers in other

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words 10 is the same thing as 2 times 5

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and 24 is the same thing as 2 times 12

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so anytime you have that and these are

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called factors again okay now where the

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this 10 can be written as a product of

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these numbers these are the factors of

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this number here but anytime you have

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the same factor in both the numerator

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and denominator we could do something

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called cross cancel essentially just get

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rid of them and then whatever is left is

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the answer okay this is more the

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simplified fraction so 1024 is

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equivalent to the fraction 512 okay so

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we talked about the basic part so far

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our fractions numerator denominator

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proper fraction improper fraction mixed

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number and now simplifying so remember

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when you're dealing with fractions you

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always want to work with fractions in

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our simplest forms or your final answer

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you want to reduce okay all right let's

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move on to number four okay so hopefully

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I can get the Sun in seven minutes I may

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go over a little bit but just think

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you'll you'll understand fractions here

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crash course alright so now we have two

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fractions here doesn't make a difference

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if they're improper proper okay but the

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idea is we want to multiply them so I

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have one fraction and I want to multiply

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it by another fraction this is very easy

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okay

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all you need to do is simply multiply

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the respective numerators and

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denominators so two times three is six

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five times four is twenty okay and then

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here this is a valid correct answer

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however you always want to simplify your

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answers reduce it

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okay this was kind of brings us back to

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the previous problem so you can think of

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six as what two times three is I just

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wrote this in twenty I can think of well

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I think it's five times four but I can

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also think of as two times ten okay so

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I'm looking to create kind of common

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factor so I could cross cancel and I'm

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left with the fraction 3/10 okay so 3/10

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is the simplified version of 6 xx

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mathematically they're equivalent okay

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but you always want to leave your final

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answers fully reduced or simplified okay

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so we got multiplication down let's talk

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about division so division is actually

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quite easy as well what we do with

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fractions is we don't actually divide

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fractions we're going to turn this

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problem into a multiplication problem

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and because the previous problem here I

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showed you how to multiply so we only

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know how to do that I'm gonna we're

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going to turn this into a multiplication

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problem then we're going to do what we

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did in pron them before so what we do

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there it's very easy is we write the

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first fraction again that's 3

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8.now we're gonna change the division

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sign here into multiplication now here's

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the deal in order to change this from

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division to multiplication you have to

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take this fraction to the right of the

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symbol the division symbol and flip it

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upside down it's called the reciprocal

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or inverse just flip it upside down so

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that's gonna be 10 over 6 okay so now I

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have a multiplication problems I'm going

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to do what I did in prom before ok I'm

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simply going to multiply the respective

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numerators and denominators so 3 times

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10 is 30 and 6 times a 8 times 6 excuse

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me is 48 and then I would go ahead and

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simplify okay I'm actually going to skip

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that right now because I want to try to

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see if I can finish this video up in a

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pretty timely manner however we would

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want to simplify as I showed you in

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prams 3 and 4 okay but technically

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speaking all right this is a correct

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answer now let's kind of stop and pause

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if you think about the operations that

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we do with numbers ok infractions are

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nothing more than numbers we multiply we

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divide we add and we subtract so as I

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showed you with fractions multiplication

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and division are effectively the same

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step we have to take an extra step with

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division but we end up just multiplying

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the same thing is going to be true with

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addition and subtraction effectively

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you're going to do the same things now

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for the purposes of this video because

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I'm one a Lumpkin I'm directing this

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video towards somebody who is like maybe

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totally forgot fractions or really

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struggling but I'm gonna teach you a way

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to add and subtract fractions that we're

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gonna bypass what they kind of teach you

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in school as far as the lowest common

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denominator and all that kind of good

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stuff so I'm gonna give you a shortcut

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method the idea here is that I'm just

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giving you a procedure to use that

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you'll get these problems right every

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time

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ok so let's talk about addition and

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subtraction procedure is the same okay

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no matter what whether whether you're

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dealing with adding or subtracting so

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here it goes it's called the bo time

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so the way it works is this you start

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with this number down here okay so it's

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the fraction to the right okay actually

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doesn't have to be in this particular

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order but this is the way I do it I

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would suggest you do it my way and just

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remember the this procedure is three

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steps and you'll be done so it's going

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to be this number of times this number

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so let's go ahead and write that here so

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five times two is what ten we'll write

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that there this is an addition problem

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so I'm going to write a plus then you're

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going to take this number and we're

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going to multiply across this way okay

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in a diagonal fashion so 3 times 7 is 21

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okay

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this is our numerator so we're gonna

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draw a little fraction bar now to get to

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our denominator we just simply multiply

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the bottom numbers okay so 3 times 5 is

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15 and we just simplify this 10 times 21

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is 31 over 15 and you're done that is it

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so this is a great method because when

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you're dealing with algebra by the way

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we just say one other thing here you

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would want to simplify this answer so if

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you got an answer let's say 30 over 48

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or something you want to simplify the

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answer the disadvantage for using this

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method for all proms is that sometimes

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you won't be you'll you'll get a

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fraction it doesn't have the lowest

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common denominator so technically you

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still need to understand that if you're

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in a algebra course or whatnot but doing

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it by adding fractions this way you'll

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get them right every single time

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and by the way let's just take a look at

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a quick algebra problem let's say I have

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something like this so you may not

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understand this completely but if I want

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it to add these fractions I go x times X

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I'm following the same step x times X

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happens to be x squared okay

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y times Z sorry this is addition

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problems so it's going to plus y times Z

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is why Z over Y times X and that's it

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this is a great method I refer to it as

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a bowtie method

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so you definitely want to learn this or

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keep this in your kind of like back

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pocket okay so if you forget anything

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about fractions you can always do this

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for addition and subtraction okay let's

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do this last problem here we're using

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the exact same method starting with this

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bottom number we're gonna go this way

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eight times three is what 24 now because

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this is a subtraction problem we need we

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need to use the subtraction operator so

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that's gonna be four times one we're

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doing the exact same steps as a previous

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problem is four over that's our

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numerator of four times eight which is

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what 32 so our answer is going to be 20

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over 32 and of course we can reduce this

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okay 20 is the same thing as 4 times 5

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and 32 is the same thing as 4 times 8 so

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I have these common factors which I can

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cross cancel and I'm left with my final

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answer whoops and about them I don't

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live with my final answer five-eighths

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okay and that is it okay so really

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fractions I'm not sure how long this

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video is gone but you pretty much

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learned a month's worth of fractions

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crash course hopefully I was I'm sure

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I'm over seven minutes but who cares the

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deal is that you know what you probably

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like remember all the stuff that you had

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to go through now there is obviously a

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few other things that you need to know

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with fractions and just make one other

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comment here let's suppose you had a

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problem like 3 and 1/2 divided by 2 and

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one thirds okay so you're like well how

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do I deal with that you know I don't see

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how I you know whether this is adding

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subtracting multiplying dividing the

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deal is with these mixed numbers just

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convert them into improper fractions so

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3 and 1/2 is the same thing as what's 3

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times 2 is 6 plus 1 7 halves divided by

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this is going to be 6 plus now this is

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actually the same thing right so 6

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is seven-halves okay so you would just

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this is a just kind of worked out way I

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just picked these random numbers but you

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get the idea this is the same thing as

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that this is the same thing as that and

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then you would do this problem using the

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steps I just showed you

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okay so finish this video up I hope that

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you find this video useful and you

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subscribe to my channel I do a ton of

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math science stuff mostly kind of math

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so my backgrounds of math math math

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teacher but I'm trying to help out those

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of your like are really struggling and

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you just need some kind of basic crash

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course just to do problems and when it

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comes to fractions this is certainly

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helpful and if you like this video

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please give it a thumbs up and let me

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know how it goes let me know if this is

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actually helping you so good luck with

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you good luck with your fractions and

play14:09

hope to see you soon

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FractionsMath BasicsQuick ReviewMixed NumbersImproper FractionsSimplifyingMultiplicationDivisionAdditionSubtraction