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Math Group

on 3 May 2013

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Addition with fractions more than one whole Addition I am going to teach you how to add fractions less than one. It is simple if you follow these steps.

Your question is 2/9 + 3/6 ( They are both proper fractions because the numerator is less than the denominator.

Step 1: Look at both of your fractions that you are adding, and see if there denominators are the same.
2/9 + 3/6 (The denominators are not the same)
Step 2: If your denominators do not consist of the same number, you are now going to find the least common multiple of each denominator, which is the least whole number that has two or more given numbers as factors.
2/9 + 3/6 multiples of 9: 9,18 multiples of 6: 6,12,18
The LCM for 9 and 6 is 18.
Step 3: Now that you have found a LCM you are going to put it as your denominator on both sides.
/18 /18
Step 4: Next you are going to take the denominators from your question (9,6) and you are going to figure out what number you have to multiply the denominators to get your new denominators number (18) on both sides.
Step 5: Next step is to multiply the number that you got from step 4, and multiply it by the numerator to get your new numerator
2/9 = 4/18 multiply by 2. 3/6 = 9/18 multiply by 3.
Step 6: You are now able to add your fractions because your denominators are the same.
4/18 + 9/18 = 13/18 Your denominators stay the same, just add your numerators.
Step 7: Your final step is to simplify your fraction if possible. Simplify means to reduce the fraction that you have to the lowest terms by finding a equivalent fraction in the which the numerator and denominator are as small as possible.
13/18 - You can not simplify this fraction because i divided the numerator and the denominator by the same number and i was getting decimal numbers, and when you reduce your fraction it has to be with whole numbers.
-Clara M Intro Hello and thank you for watching our prezi all about fractions. If you continue reading, you will learn how to add, subtract, multiply and divide with fractions. You will also learn how to problem solve along with some practice questions. At the end of this prezi, we are sure you will understand everyone! Next we can subtract our numerators since the denominators are the same!
4/6 - 1/6
= 3/6
Now we have to simplify and then we are done!
and box your FINAL answer!
Here are the steps:
1. Are the denominators the same?
2. If yes, subtract your numerators, simplify(if possible) box your answer and done!
3. If no, find your lowest common denominator.
4. Then subtract your numerators, simplify, box your answer, and you're done!

-Jenna V. Multiplication Multiplying with fractions is very simple. Its pretty much just multiplying as if it were'nt a fraction.

When multiplying with fractions, you always multiply the numerator(n) by numerator and denominator(d) by denominator. For exemple:

n x n, d x d 4/6 x 2/3 = 8/18

Now before bow our final anwser, make sure its in its simplest form. So it will equal 4/9 by dividing the n and d by 2. Now we can bow our final answer.
4/6 x 2/3
= 8/18
= 4/9

If you multiply with a whole number and a fraction, lets say 2 x 2/6, you always put the whole number over 1. So noe its 2/1 x 2/6. Then you will just multiply normally.
2/1 x 2/6
= 4/6 make sure to put it in simplest form
=2/3 then box your anwser
-Sabrina B. By: Jenna, Clara, Sabrina and Abby Fractions Multiplying : 1)1 1/14 2) 3/8 3)1 6/8 4) 24/10

Adding: 1)1 1/3 2)1 11/12 3)6 7/18 4)3 5/12

Dividing: 1)1 1/9 2)11/15 3)3/5 4)7/12

Substracting: 1) -2/5 2)1/2 3)1/3 4)-1 3/4 Multiplication Order of operations Definitions Subtraction with fractions less than one whole Subtraction with fractions less than one is the exact same as addition with fractions less than one. Let's go through an example together:
2/3 - 1/6 So first you ask yourself, "are the denominators the same?" If they are the same, just subtract the numerators, simplify and you're done. But in this case the denominators aren't the same so we have to find a common denominator between 3 and 6. So let's make our list of multiples of 3 and 6.
3: 3,6,9,12
6:6,12,18 So our first match was 6!

Now we will make equivalent fractions with the denominator of 6. 1/6 is already in sixths so we don't have to do anything but we have to make 2/3 out of sixths so we will multiply the numerator and denominator both by 2.
4/6 - 1/6
-Jenna V. Subtracting with fractions more than one whole Adding fractions more than one whole is almost the same as adding fractions, but you have one more extra step!

Here is an example: 2 1/5 + 3 2/10

Step 1: You are going to add your 2 whole numbers together and leave them on the side until your last step.
2+3= 5
Step 2: You are now going to solve your 2 fractions the same way you would.
1/5 + 2/10 multiples of 5: 5,10 multiples of 10: 10 LCM= 10

1/5= 2/10 2/10 = 2/10 2/10 + 2/10= 4/10
Reduce your fraction if possible: 2/5 ( divide by 2)

Step 3: Your final step is to add in your whole number that you got in step one. (5)
5 2/5
If you have a improper fraction that you reduced you have to turn in into a mixed number.
Here is a example: 13/9
First you divide your numerator (9) by your denominator (13) .
9 goes into 13 once, and your remainder is 4. The number of times 9 goes into 13 is going to be your whole number. Your remainder will be your numerator. And your denominator is the same denominator as in your fraction.

Your final answer would be 1 4/13

-Clara M Proper Fraction: Numerator is less than the denominator

Improper Fraction: Numerator is greater than or equal to denominator

Equivalent Fraction: Fractions that represent the same number

Fraction: Part of a whole the bottom number says how many parts the whole is divided into and the top number says how many you have

Denominator: The number that is on the bottom of your fraction example: 3/4 ( 4 is your denominator)

Numerator: The number that is on the top of your fraction example: 2/9 ( 2 is your numerator)

Least common multiple (LCM): The least whole number that has two or more given numbers as factors(eg.12 is the least common multiple of 4 and 6)

Reduce: Reduce a fraction to the lowest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible

multiple: The product of a whole number and any other whole number (eg. when you multiply 10 by the whole numbers 0 to 4, you get the multiples 0,10,20,30,and 40

Whole numbers: The counting numbers that begin at 0 and continue forever o,1,2,3...

Reciprocal: The opposite fraction when flipped ( 3/4 4/3). When you multiply two reciprcol fractions, the product is always 1!
-Clara M Divison Practice Questions: Multiplying : 1) 5/7 x 3/2 = 2) 1/2 x 3/2 = 3) 1 3/4 x 1 1/2 = 4) 8/5 x 3/2 =

Adding: 1) 1/2 + 5/6 = 2) 1 3/4 + 1/6 =
3) 2 1/2 + 3 8/9 = 4) 7/4 + 5/8 =

Dividing: 1) 5/6 / 3/4 = 2) 1 1/2 / 2 2/4 = 3) 6/4 / 5/2 = 4) 7/8 / 9/6 =

Substracting: 1) 1/2 - 9/10 = 2) 2/1 - 3/2 = 3) 1 5/6 - 1 1/2 = 4) 5/4 - 3/1 = Review Now you should be able to add, subtract, multiply and divide fractions less than one (ex. 3/4) and more than one (ex. 3 4/5 and 9/3)
So, here are some tips and things to remember:
- You always have to simplify or else the answer isn't complete.
-You can never have an improper fraction as a final answer/product so always change the improper fraction into a mixed number.
-line up your equal signs
-box your FINAL answer.
The steps:
-change improper fractions into mixed numbers, then add thw whole numbers and set them aside
-are the denominators the same?
-if yes add or subtract the numerators.
-if no, find the lowest common denominator
-add a whole if needed for subtraction, add the wholes that were left earlier, simplify and done!
-change mixed numbers to improper fractions
-DIVISION- get the reciprocal of the second fraction, flip the sign to multipulcation
-multiply numerator x numerator and denominator x denominator
-simplify and done! If your multiplying with a mixed fraction, lets say 2 3/4 x 4/6, you have to change the mixed fraction into an improper fraction, so now it becomes 11/4 x 4/6. Then you will just multiply normally.
11/4 x 4/6
=44/4 Now you change it into a mixed fraction.
=1 5/6 (simplest form)

If you find multiplying this way to easy or to hard, heres another way called crossed multiplication. Lets say our equation is 3/4 x 8/12. Which is were you would look at the denominator of the first fraction, and the nemorator of the second and see if they are multiples. If so, you see what you can divide both numbers by the same number. Then you would do the opposite for the other fraction. So ;

3/4 x 8/12 4 divided by 4 = 1 & 8 divided by 4 = 2
=2/4 3 divided by 3 = 1 & 12 divided by 3 = 4
=1/2 * but it only works if they can both divide even ually by the same number. *

Sometimes you ma get the same fraction multiplied by its self. So for exemple 3/4 x 3/4, you could always just change it into exponents. So it would be (3/4)2.
(3/4) 2 x 2/3 start with exponents
=3/4 x 3/4 x 2/3 multiply first 2 fractions
=9/16 x 2/3 then these 2 fractions
=18/48 then put reduce this
=3/8 simplest form
-Sabrina B. For order of operations you are going to use BEDMAS, to get the proper answer.
Step 1; follow BEDMAS starting with brackets.
-> (1/2 + 3/4) 2 x 2/3 divided by 3/9 - 1/2
Step 2; solve whats in the brackets.
(2/4 + 3/4) 2
= 5/4 x 5/4
Step 3; solve your exponents(always multiplication)
25/16 x 2/3 divided by 3/9 - 1/2
Step 4; next solve multiplication/division
25/16 x 2/3
=50/48 divided by 3/9 - 1/2
Step 5; next solve your division
50/48 divided by 3/9
= 50/48 x 3/9
=450/144 - 1/2
Step 6; subtract
450/144 - 1/2
=450/144 - 72/144
Step 8; reduce if possible * if its an improper fraction, change it to a mixed fraction.
378/144 divided by 8 = 21/8
=2 5/8. B- brackets
E- exponents
D- division
M- multiplication
A- addition
S- subtraction This is when it gets a little tricky but when you follow these steps it will Let's go through an example.
2 2/3 - 7/4 We can't have mixed numbers in this expression so we will change the improper fraction into a mixed number
2 2/3 - 1 3/4 Next we will subtract our whole numbers ( 2-1) and leave it on the side.
So, now we will subtract normally like we did for fractions less than one!
2/3 - 3/4 But now we have a problem! if you subtract 9 from 9 you get a negative number! So we
= 8/12- 9/12 have to take a whole from the one that we saved earlier and add it to the 8/12
=8/12 + 12/12
=20/12 - 9/12 Now we can subtract normally!
=11/12 Simplify if possible, (in this case we can't) box your answer and you're done!
But wait, remember that 1 we saved earlier? Well since we had to take a whole from it its now a zero so it's gone! If there was a number left over then just make that the whole for the mixed number.

The steps:
1. Change all improper fractions into mixed numbers.
2. Subtract your whole number and put them to the side.
3. Subtract your fractions normally but add a whole if needed.
4. Put your whole number into the answer, simplify if possible and box your answer
Remember: If your answer is a mixed number BEFORE you add your whole number, add your whole number to the whole of the answer!
-Jenna 1 0 Problem Solving It may seem a little difficult to answer word problems but you just have to think about what you have to do! We will be using the format of Given, Solve, Statement to organize our work. In given, your write what you know or the key information and what the question is asking you. In solve you show your work on how you solved the problem and finally in statement you write your answer in sentence form.

Question: The Hubba Bubba bubble gum tape is 6 feet long. How many 2 1/4 peices of the tape can be cut into the 6 feet of tape?

Given: Solve: Statement:
-tape= 6 feet long 6 ÷ 2 1/4 We can cut 2 whole pieces into the 6
-2 1/4 peices =6/1 ÷ 2 1/4 feet but there will be 6/9 leftover.
How many peices =6/1 x 4/9
can we cut in =2 6/9
the 6 feet? Answers to practice questions Dividing a proper fraction:
Let's say we have: 1/2 / 3/4

K: keep the first
F: 'flip' the second
C: change the sign

These will be the steps you will follow.

Step 1. First, you need to keep the first fraction (1)
Step 2. You will need to flip the second fraction, in other words, you flip the numertor and the denominator so they are reversed. (4/3)
Step 3. And last, you have to change the sign into a multiplycation. ( x )
Step 4. After you have finished all your steps, you can add them up.
Step 5. First, multiply the numerator from the first fraction by the numerator from the second fraction. ( 1x4 )
Step 6. After that. you will do the same with the denominators. ( 2x3 )
Step 7. Once you have both answers, you make them in a fraction. ( 4/6)

If your fraction can be simplyfided, meaning, your numerator and denominator can divide by the saame number to make the lowest numbered fraction possible.

For 4/6 it can be divided by 2. ( 2/3 )
Once you have your answer, you must box your answer after words. / = Division sign This is how it should look ;

1/2 / 3/4

= 1/2 / 4/3

= 1/2 x 4/3

= 4/6

= 2/3 Divinding a whole fraction Lets say you have: 1 1/2 / 1/2

Dividing a whole fraction is much like dividing a regular proper fraction. You must make the whole fraction into an improper fraction by multiplying the whole number ( which is 1 ) by the denominator ( which is 2 ) followed by adding the numerator ( wich is 1 ).
your answer should be 3/2.

To divide the following ( 3/2 / 1/2 ) itwould be the same as dividing a regular proper fraction. This is how it should look ;

1 1/2 / 1/2

=3/2 / 1/2

= 3/2

= 6/2

= 3 / = divison sign Diving one whole fraction If you only have a whole fraction ( 4 / 1/2 ) all you need to do is put the whole fraction on one (1)

4/1 / 1/2

After all you need to do is repeat the same steps as you would for the improper fractions. / = divison sign
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