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# Fractions

How to add, subtract, multiply and divide fractions with order of operations

#### Transcript of Fractions

You have not finished yet there is one more step...

simplify. Simplify means to make the fraction in its simplest form you must divide the top and the bottom by the same number.

IT CAN NOT BE A DECIMAL! Your teacher will probably take off marks if you don't simplify!

Note - Box your answer so your teacher knows your final answer. Fractions Terms Step 1 Preparing the Equation the first step is to write out the question, if their is a mixed number in the equation change it to a improper fraction. to challenge a mixed number to a improper fraction you multiply the denominator by the whole number and add the product to the numerator (look at board for example). If there are any whole numbers just turn it into a fraction by putting that number as the numerator and 1 as the denominator (see board for example ) Step 2 Multiplying the Fractions One you have changed all mixed numbers to improper fractions and whole numbers to fractions you simply multiply the two denominators together and have the product be your new denominator (see board for example). Now you do the same for the numerators, multiply the two together and have the product be your new numerator Step 3 Simplifying if you have a fraction, simplify it by finding numbers that both numerator and denominator can be divided by then divide until the fraction is in simplest form. if you have an improper fraction change it to a mixed number by dividing the denominator into the numerator evenly and having the quotient be your whole number and the remainder be your numerator and keep the denominator the same. now if possible simplify your fraction by finding a number that both numerator and denominator can be divided by and doing that until the only common factor is 1 (see board for example) Review -mix number to improper fraction

-numerator x numerator

-denominator x denominator

-improper fraction to mixed number (if necessary)

-simplify fraction- a numeral equation that is not a whole number

product-the answer to a multiplication question

lowest terms-a fraction with both numerator and denominator at simplest form

simplest form-a fraction is in its simplest form when both numerator and denominator are whole numbers and the only common factor is 1

mixed number- a mathematical expression where their is a whole number and a fraction Dividing Fractions Dividing fractions is the easiest to remember. You will first need to know how to K. F. C the question. K F C stands for :

K - Keep the first fraction exactly as it is

F - Flip the second fraction Ex: 2/1 = 1/2

C - Change the sign from division to multiplication x- ÷ Step 2 : Multiply Across once you have K F C' d your fraction you must now multiply across : 2 x 1 = 2

3 x 2 = 6 Step 3 : simplify Dividing Fractions Definitions numerator - the top number in a fraction

denominator - the bottom number in a fraction

quotient - the answer of a division question

proper fraction - fraction where the numerator is smaller then the denominator

improper fraction - fraction where the numerator is bigger then the denominator

mixed number - number where the nominator is more the once the denominator Resume K - Keep the first fraction

F - Flip the second fraction

C - change the sign from division to multiplication

multiply across

simplify

change it to a mixed number

box your answer Adding Fractions Terms Fraction : A number less than 1; a part of a whole

Proper Fraction : A fraction in which the numerator is less than the denominator

Improper Fraction : A fraction in which the denominator is less than the numerator

Mixed Number : A number consisting of a whole number and a proper fraction

Numerator : In a fraction, the number on the top or to the left indicating the number of parts of a whole indicated by the denominator

Denominator : In a fraction, the number on the bottom or to the right

Sum : the answer to an addition equation

LCM : The lowest number that is a multiple of 2 or more numbers, for example, the LCM of 2 and 3 is 6

LCD : The LCM of the denominators of various fractions

Equivalent Fractions : Two or more fractions that are equal, for example, 1/3 and 2/6 are equivalent fractions

Lowest Terms : The lowest form of a fraction in which the only common factor of the numerator and denominator is 1

GCF : The largest number that divides evenly into 2 or more numbers, for example, the GCF of 8 and 12 is 4 Your Steps: We need an O.O.O. Section!!! Mixed Number to Improper Fraction and Vice Versa To change a mixed number to an improper fraction, you will multiply your denominator by your whole number, and add the product to your numerator. The denominator of your improper fraction stays the same. Ex : 1 2/3 1 x 3 = 3 3 + 2 = 5 1 2/3 = 5/3 To change an improper fraction to a mixed number, you will divide your numerator by your denominator WITH A REMAINDER. The quotient of your equation is your whole number, your denominator stays the same, and your remainder is your new quotient. Ex : 9/4 9 ÷ 4 = 2 R1 9/4 = 2 1/4 Finding your LCD and Reducing to Lowest Terms To find your LCD, you must find the LCM of your two denominators. You will do so by listing the multiples of your two denominators. 4 : 4, 8, 12 3 : 3, 6, 9, 12 When you come across your first, or lowest match, you have found your common denominator. You then multiply your denominators so that they equal your LCD. you then proceed to multiply your numerators by the number you multiplied the denominator of the same fraction by. 1/3 + 3/4

= x/12 + y/12 3 x 4 = 12 1 x 4 = 4 x = 4 4 x 3 = 12 3 x 3 = 9 y = 9 1/3 + 3/4

= 4/12 + 9/12 Finally, add as normal. To reduce to lowest terms, divide your numerator and denominator by their GCF. Your new fraction is in lowest terms. 16/20 1/3 + 3/4 16 : 1, 2, 4, 8, 16 20 : 1, 2, 4, 5, 10, 20 The GCF is 4. 16 ÷ 4 = 4 20 ÷ 4 = 5 16/20 = 4/5 Example Question: 2/3 + 6/7 Following our steps, we must find a common denominator. 3 : 3, 6, 9, 12, 15, 18, 21 7 : 7, 14, 21 Now we convert the fractions. 2/3 = x/21 3 x 7 = 21 2 x 7 = 14 x = 14 6/7 = y/21 7 x 3 = 21 6 x 3 = 18 y = 18 14/21 + 18/21

= 32/21 And add as normal. Since our answer is an improper fraction, we must change it to a mixed number. 32/21 = 1 11/21 This answer is in lowest terms, so we can box it, as it is our final answer. 2/3 + 6/7 = 1 11/21 Subtracting Fractions:

When subtracting fractions you need to look if there is a whole number or not. If there is whole numbers, then just subtract them. If there isn't any then you font need to worry and if there's one whole number then you don't need to do anything to it.

After you subtract your whole numbers, put the answer aside, we don't need it now and will come back to it later.

Ex. (4 1/4 - 1 1/3) 4-1=3. Now you would put 3 aside for later since it's the answer after subtracting your wholes, 4 and 1. dividing with mixed numbers Dividing with mixed numbers is the same as dividing without them but you need to make the fraction an improper fraction. The large number in your fraction is your whole number. To change the mixed number into an improper fraction you need to multiply your denominator by your whole number then add your numerator. you keep the same denominator. Once you have changed it into a improper fraction you can now continue with your K F C. If you have a whole number but that does not look like a fraction you make it out of one. ex : 3 = 3/1 After you finish with the whole numbers we are going to need to look at the denominators of your fractions that you're subtracting. The denominator is the bottom number of the fraction and represents your whole.

Ex. (1/2) In this fraction, 2 is the denominator.

If your denominators are not the same number, you're going to need to find something in between them called the "Lowest Common Denominator" or "LCD" for short.

The LCD is the first number that both your fractions can be put into.

ex. (1/2 - 1/4) The LCD for the given equation is 4. It's 4 since 4 goes into itself once and 2 goes into 4 aswell. It's the first number that they both go into.

We'll get back to this in a minute tho. If your denominators are the same then you subtract your numerators.

The numerator is the top number of the fraction and shows how much you have of something out of your whole.

In the fraction above, the denominator would be 4 since that's the amount of slices there is which is also your whole and the numerator would be 1 since only one slice is shaded. Your fraction is 1/4. If your denominators in the fractions that your subtracting are the same, subtract the numerators of the fractions and put the answer from that over the denominator. Remember that you can't subtract unless your denominators are the same.

Ex. (3/3 - 1/3) Now, since the denominators are the same, i'm all ready to subtract. So 3-1 = 2. Now that i have my answer which in this case was 2, i put it over my denominator. 2/3.

Once you're done that, were going to need to bring the whole numbers you saved from the beginning back in. From the example before, our whole number was 3 so all we have to do is put it in front of the fraction. 3 2/3.

If your numerator is larger then your denominator it means you have more then a fraction since it's greater then your whole. This is called an improper fraction. We can't have an improper fraction tho so we need to change it into what we call a mixed number. To do this you need to see how many times the denominator goes into the numerator then you take the leftover of that and put it over the denominator.

Ex. (8/3 = 2 2/3) 3 goes into 8 twice so that's your whole number then you have a leftover of 2 which you put over your original denominator, 3.

Once you have your answer you need to put it into lowest terms by dividing each side, if you can.

Ex. (6/8 =3/4, 4/12 = 1/3)

There you go, you have your answer and don't forget to box it! :) If the denominators are NOT the same you have to find your LCD. ( refer back to earlier slide if you don't know how to find the LCD.)

Once you find the LCD between your denominators, you have to see how many times the denominators went into it.

Ex. (3/7 - 2/4) 7 goes into the LCD which is 28, 4 times and 4 goes into the LCD 7 times.

Since whatever you do to the bottom number you have to do the top number, you see how many times the denominator went into the LCD, let's just say it went into it 7 times, you would have to multiply the numerator by 7 as well.

Ex. (The LCD in between 3/4 - 3/8 is 8. Since for 4 to get it into 8, you multiply by 2, you have to multiply 3 by 2 as well. You don't need to do anything to 3/8 since 8 is the LCD ( 8 goes into 8 once..) so now we have 6/8 - 3/8 which would equal 3/8.)

So to resume that once you get your LCD then multiply the numerator by how many time it took the denominator to get into the LCD, subtract and then you're done!! Once again, don't forget to box your answer!!!!! :D 2 3 4 multiply add = 11 4 Practice questions 1) Charlie wants to share her 8 chocolate bars with 9/10 of her class how many pieces will they each get?

2) what is 6/9 0f 6/3 ?

3) I have 5 and a half dollars and I want to spend 2/5 of that money how much will I spend ?

Order of Operations Order of operation is easy to do if I can do it you can to. All you will need to pass is to remember to use B E D M A S. B - stands for brackets witch you always do first

E - stands for exponents they are never the worst

D - stands for division that is always fun

M - stands for multiplication you do them both as one

A - stands for addition as easy as one plus one

S - stands for subtraction is the last and your done

Full transcriptsimplify. Simplify means to make the fraction in its simplest form you must divide the top and the bottom by the same number.

IT CAN NOT BE A DECIMAL! Your teacher will probably take off marks if you don't simplify!

Note - Box your answer so your teacher knows your final answer. Fractions Terms Step 1 Preparing the Equation the first step is to write out the question, if their is a mixed number in the equation change it to a improper fraction. to challenge a mixed number to a improper fraction you multiply the denominator by the whole number and add the product to the numerator (look at board for example). If there are any whole numbers just turn it into a fraction by putting that number as the numerator and 1 as the denominator (see board for example ) Step 2 Multiplying the Fractions One you have changed all mixed numbers to improper fractions and whole numbers to fractions you simply multiply the two denominators together and have the product be your new denominator (see board for example). Now you do the same for the numerators, multiply the two together and have the product be your new numerator Step 3 Simplifying if you have a fraction, simplify it by finding numbers that both numerator and denominator can be divided by then divide until the fraction is in simplest form. if you have an improper fraction change it to a mixed number by dividing the denominator into the numerator evenly and having the quotient be your whole number and the remainder be your numerator and keep the denominator the same. now if possible simplify your fraction by finding a number that both numerator and denominator can be divided by and doing that until the only common factor is 1 (see board for example) Review -mix number to improper fraction

-numerator x numerator

-denominator x denominator

-improper fraction to mixed number (if necessary)

-simplify fraction- a numeral equation that is not a whole number

product-the answer to a multiplication question

lowest terms-a fraction with both numerator and denominator at simplest form

simplest form-a fraction is in its simplest form when both numerator and denominator are whole numbers and the only common factor is 1

mixed number- a mathematical expression where their is a whole number and a fraction Dividing Fractions Dividing fractions is the easiest to remember. You will first need to know how to K. F. C the question. K F C stands for :

K - Keep the first fraction exactly as it is

F - Flip the second fraction Ex: 2/1 = 1/2

C - Change the sign from division to multiplication x- ÷ Step 2 : Multiply Across once you have K F C' d your fraction you must now multiply across : 2 x 1 = 2

3 x 2 = 6 Step 3 : simplify Dividing Fractions Definitions numerator - the top number in a fraction

denominator - the bottom number in a fraction

quotient - the answer of a division question

proper fraction - fraction where the numerator is smaller then the denominator

improper fraction - fraction where the numerator is bigger then the denominator

mixed number - number where the nominator is more the once the denominator Resume K - Keep the first fraction

F - Flip the second fraction

C - change the sign from division to multiplication

multiply across

simplify

change it to a mixed number

box your answer Adding Fractions Terms Fraction : A number less than 1; a part of a whole

Proper Fraction : A fraction in which the numerator is less than the denominator

Improper Fraction : A fraction in which the denominator is less than the numerator

Mixed Number : A number consisting of a whole number and a proper fraction

Numerator : In a fraction, the number on the top or to the left indicating the number of parts of a whole indicated by the denominator

Denominator : In a fraction, the number on the bottom or to the right

Sum : the answer to an addition equation

LCM : The lowest number that is a multiple of 2 or more numbers, for example, the LCM of 2 and 3 is 6

LCD : The LCM of the denominators of various fractions

Equivalent Fractions : Two or more fractions that are equal, for example, 1/3 and 2/6 are equivalent fractions

Lowest Terms : The lowest form of a fraction in which the only common factor of the numerator and denominator is 1

GCF : The largest number that divides evenly into 2 or more numbers, for example, the GCF of 8 and 12 is 4 Your Steps: We need an O.O.O. Section!!! Mixed Number to Improper Fraction and Vice Versa To change a mixed number to an improper fraction, you will multiply your denominator by your whole number, and add the product to your numerator. The denominator of your improper fraction stays the same. Ex : 1 2/3 1 x 3 = 3 3 + 2 = 5 1 2/3 = 5/3 To change an improper fraction to a mixed number, you will divide your numerator by your denominator WITH A REMAINDER. The quotient of your equation is your whole number, your denominator stays the same, and your remainder is your new quotient. Ex : 9/4 9 ÷ 4 = 2 R1 9/4 = 2 1/4 Finding your LCD and Reducing to Lowest Terms To find your LCD, you must find the LCM of your two denominators. You will do so by listing the multiples of your two denominators. 4 : 4, 8, 12 3 : 3, 6, 9, 12 When you come across your first, or lowest match, you have found your common denominator. You then multiply your denominators so that they equal your LCD. you then proceed to multiply your numerators by the number you multiplied the denominator of the same fraction by. 1/3 + 3/4

= x/12 + y/12 3 x 4 = 12 1 x 4 = 4 x = 4 4 x 3 = 12 3 x 3 = 9 y = 9 1/3 + 3/4

= 4/12 + 9/12 Finally, add as normal. To reduce to lowest terms, divide your numerator and denominator by their GCF. Your new fraction is in lowest terms. 16/20 1/3 + 3/4 16 : 1, 2, 4, 8, 16 20 : 1, 2, 4, 5, 10, 20 The GCF is 4. 16 ÷ 4 = 4 20 ÷ 4 = 5 16/20 = 4/5 Example Question: 2/3 + 6/7 Following our steps, we must find a common denominator. 3 : 3, 6, 9, 12, 15, 18, 21 7 : 7, 14, 21 Now we convert the fractions. 2/3 = x/21 3 x 7 = 21 2 x 7 = 14 x = 14 6/7 = y/21 7 x 3 = 21 6 x 3 = 18 y = 18 14/21 + 18/21

= 32/21 And add as normal. Since our answer is an improper fraction, we must change it to a mixed number. 32/21 = 1 11/21 This answer is in lowest terms, so we can box it, as it is our final answer. 2/3 + 6/7 = 1 11/21 Subtracting Fractions:

When subtracting fractions you need to look if there is a whole number or not. If there is whole numbers, then just subtract them. If there isn't any then you font need to worry and if there's one whole number then you don't need to do anything to it.

After you subtract your whole numbers, put the answer aside, we don't need it now and will come back to it later.

Ex. (4 1/4 - 1 1/3) 4-1=3. Now you would put 3 aside for later since it's the answer after subtracting your wholes, 4 and 1. dividing with mixed numbers Dividing with mixed numbers is the same as dividing without them but you need to make the fraction an improper fraction. The large number in your fraction is your whole number. To change the mixed number into an improper fraction you need to multiply your denominator by your whole number then add your numerator. you keep the same denominator. Once you have changed it into a improper fraction you can now continue with your K F C. If you have a whole number but that does not look like a fraction you make it out of one. ex : 3 = 3/1 After you finish with the whole numbers we are going to need to look at the denominators of your fractions that you're subtracting. The denominator is the bottom number of the fraction and represents your whole.

Ex. (1/2) In this fraction, 2 is the denominator.

If your denominators are not the same number, you're going to need to find something in between them called the "Lowest Common Denominator" or "LCD" for short.

The LCD is the first number that both your fractions can be put into.

ex. (1/2 - 1/4) The LCD for the given equation is 4. It's 4 since 4 goes into itself once and 2 goes into 4 aswell. It's the first number that they both go into.

We'll get back to this in a minute tho. If your denominators are the same then you subtract your numerators.

The numerator is the top number of the fraction and shows how much you have of something out of your whole.

In the fraction above, the denominator would be 4 since that's the amount of slices there is which is also your whole and the numerator would be 1 since only one slice is shaded. Your fraction is 1/4. If your denominators in the fractions that your subtracting are the same, subtract the numerators of the fractions and put the answer from that over the denominator. Remember that you can't subtract unless your denominators are the same.

Ex. (3/3 - 1/3) Now, since the denominators are the same, i'm all ready to subtract. So 3-1 = 2. Now that i have my answer which in this case was 2, i put it over my denominator. 2/3.

Once you're done that, were going to need to bring the whole numbers you saved from the beginning back in. From the example before, our whole number was 3 so all we have to do is put it in front of the fraction. 3 2/3.

If your numerator is larger then your denominator it means you have more then a fraction since it's greater then your whole. This is called an improper fraction. We can't have an improper fraction tho so we need to change it into what we call a mixed number. To do this you need to see how many times the denominator goes into the numerator then you take the leftover of that and put it over the denominator.

Ex. (8/3 = 2 2/3) 3 goes into 8 twice so that's your whole number then you have a leftover of 2 which you put over your original denominator, 3.

Once you have your answer you need to put it into lowest terms by dividing each side, if you can.

Ex. (6/8 =3/4, 4/12 = 1/3)

There you go, you have your answer and don't forget to box it! :) If the denominators are NOT the same you have to find your LCD. ( refer back to earlier slide if you don't know how to find the LCD.)

Once you find the LCD between your denominators, you have to see how many times the denominators went into it.

Ex. (3/7 - 2/4) 7 goes into the LCD which is 28, 4 times and 4 goes into the LCD 7 times.

Since whatever you do to the bottom number you have to do the top number, you see how many times the denominator went into the LCD, let's just say it went into it 7 times, you would have to multiply the numerator by 7 as well.

Ex. (The LCD in between 3/4 - 3/8 is 8. Since for 4 to get it into 8, you multiply by 2, you have to multiply 3 by 2 as well. You don't need to do anything to 3/8 since 8 is the LCD ( 8 goes into 8 once..) so now we have 6/8 - 3/8 which would equal 3/8.)

So to resume that once you get your LCD then multiply the numerator by how many time it took the denominator to get into the LCD, subtract and then you're done!! Once again, don't forget to box your answer!!!!! :D 2 3 4 multiply add = 11 4 Practice questions 1) Charlie wants to share her 8 chocolate bars with 9/10 of her class how many pieces will they each get?

2) what is 6/9 0f 6/3 ?

3) I have 5 and a half dollars and I want to spend 2/5 of that money how much will I spend ?

Order of Operations Order of operation is easy to do if I can do it you can to. All you will need to pass is to remember to use B E D M A S. B - stands for brackets witch you always do first

E - stands for exponents they are never the worst

D - stands for division that is always fun

M - stands for multiplication you do them both as one

A - stands for addition as easy as one plus one

S - stands for subtraction is the last and your done