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math-fractions PREZI

FractionsPREZI
by

Ariane Poserio

on 3 May 2013

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Transcript of math-fractions PREZI

LCM:
The least whole number that has two or more given numbers as factors.

Ex:

•12: 12
•6: 6, 12

When doing a fraction equation involving addition or subtraction, you must find the Lowest Common Multiple.

Ex:

•2/3 + 1/2
•LCM
3: 3, 6
2: 2, 4, 6
•Your LCM is 6. Replace the Denominator with 6.
=2/6 + 1/6
•Count the amount of numbers it took to get to you LCM.
3: 3, 6. Two numbers to get to the LCM
2: 2, 4, 6. Three numbers to get to the LCM
•Multiply the Numerator with the amount of numbers you counted.
=2x2/6 + 1x3/6
=4/6 + 3/6
•Answer, DO NOT ADD THE DENOMINATORS
•=4/6 + 3/6
=7/6
•If the Numerator was smaller than the Denominator, you would leave it that way. But since the Numerator is bigger than the Denominator, you must change it to a mixed number.
•Think, how many times does 6 go into 7? The answer is one time, including 1 remainder.
=1 1/6 Least Common Multiple Converting fractions to mixed numbers and mixed numbers into fractions is very simple, but a little complicated. Take the mixed number 3 1/2 for example.

To turn this mixed fraction into a proper fraction, you will have to multiply the denominator by the whole number.

2 x 3
= 6

Then, add your numerator to that product.

2 x 3 + 1
= 6 + 1
= 7

The number 7, is your new numerator. Your old denominator stays the same.

3 1/2 = 7/2

Your improper fraction is now 7/2.

Lets turn 7/2 back into a mixed number. To do this first, you must divide the numerator by the denominator.

7 ÷ 2
= 3.5

Sometimes, when doing this, the digits after the decimal can get complicated. So just ignore them. The number before the decimal is your whole number. We know that the whole number is 3, and that the denominator is 2, but what is the numerator?

Multiply your whole number by the denominator.

3 x 2
= 6

Using that product, subtract it from your old denominator.

3 x 2
= 6
= 7 - 6
= 1

The difference than you got will be the new numerator. So:

7/2
= 7 ÷ 2
= 3.5
= 3 _/2
= 3 x 2
= 6
= 7 - 6
= 1
= 3 1/2

3 1/2 can not be reduced any further; therefore it is our new mixed number. Converting Fractions into Mixed Numbers and Mixed Numbers into Fractions Using an improper fraction is another way of expressing a mixed number.

Improper fractions are fractions in which the numerator has a greater value than the denominator.

For example; 7/3 is an improper fraction.

To turn an improper fraction into a mixed number (a number that contains a whole number and a fraction), you divide the numerator by the denominator. The quotient - without the remainder - is the whole number of the mixed number. The remainder is the numerator of the fraction, and the denominator of the improper fraction remains constant.

For example; 7/3
= 7÷3
= 2 Remainder=1
= 2 1/3

7÷3 equals 2 with a remainder of 1. Therefore the 2 becomes the whole number, the 1 becomes the numerator, and the 3 remains the denominator. 7/3 as a mixed number is 2 1/3.

-21/7
= -21÷7
= -3 Remainder=0
= -3 0/7
= -3

-21÷7 equals -3 with no remainder. Therefore the -3 becomes the whole number, the 0 becomes the numerator, and the 7 remains the denominator. -21/7 as a mixed number is -3 0/7, which can be simplified to -3. Improper Fractions
Equivalent fractions are important when it comes to
addition, subtraction, and simplification.

Equivalent fractions are two or more fractions that are equal to one another.

For example; 1/3, 2/6, and -3/-9 are equivalent fractions.

To determine equivalent fractions, you multiply or divide both the numerator and the denominator of the original fraction by the same scale factor.

For example; 1/3 = 2/6. 1x2=2, 3x2=6. You multiply both the numerator and the denominator of 1/3, so 1 and 3, by a scale factor of 2 to give you the equivalent fraction of 2/6.

1/3 = -3/-9 = 3/9. 1x(-3)=(-3), 3x(-3)=(-9). You multiply both the numerator and the denominator of 1/3, so 1 and 3, by a scale factor of -3 to give you the equivalent fraction of -3/-9 which is also equal to 3/9.

To get the lowest terms of a fraction, you divide both the numerator and the denominator by the same scale factor.

For example; 6/24 = 1/4. 6÷6=1, 24÷6=4. You divide both the numerator and the denominator of 6/24, so 6 and 24, by a scale factor of 6, therefore 6/24 in lowest terms is 1/4. Equivalent Fractions Converting Fractions into Decimals and Decimals into Fractions Addition Subtraction Division By Lucia By Lucia By Lucia Fractions The division of fractions is important when you find yourself in real life situations such as decreasing a recipe while keeping the same ratio of ingredients or splitting a cake or a pizza.

The dividend is the first number in a division question. The dividend is divided by the divisor. The divisor is the second number in a division question. The divisor divides the dividend. The quotient is the answer to a division question.

For example; 2/3÷1/2 = 1 1/3. 2/3 is the dividend, 1/2 is the divisor, and 1 1/3 is the quotient.

To divide fractions, you turn the division question into a multiplication question. The dividend remains the same, the division operation turns into a multiplication operation, and the numerator of the divisor becomes the denominator of the divisor, and the denominator of the divisor becomes the numerator of the divisor. Therefore you multiply the dividend by the reciprocal of the divisor. A reciprocal is the result of flipping a fraction.

For example; 2/3 ÷ 1/2
= 2/3 x 2/1

Then you multiply. A product is the answer to a multiplication question. To multiply fractions you multiply the numerators of both fractions to get the numerator of the product, and the denominators of both fractions to get the denominator of the product. Then you simplify.

For example; 2/3 ÷ 1/2
= 2/3 x 2/1
= (2x2)/(3x1)
= 4/3
= 1 1/3

The division operation is changed to a multiplication operation and the numerator and denominator switch in the divisor. 2/3x2/1 equals (2x2)/(3x1). 2x2 equals 4 and 3x1 equals 3. 4/3 can be simplified from an improper fraction to a mixed number of 1 1/3.

5/6÷(-4/5)
= (5/6)x(5/-4)
= (5x5)/(6x[-4])
= 25/-24
= -1 1/24

The division operation is changed to a multiplication operation and the numerator and denominator switch in the divisor. 5/6x5/-4 equals (5x5)/(6x[-4]). 5x5 equals 25, and 6x(-4) equals -24. 25/-24 can be simplified from an improper fraction to a mixed number of -1 1/24.

To divide fractions with mixed numbers, you turn the mixed number into an improper fraction, and then you turn the division question into a multiplication question, multiply, turn the fraction back into a mixed number if needed, and simplify.

For example; 1 1/2 ÷ 2 3/4 is changed to an expression with improper fractions. Therefore the expression now is 3/2 x 11/4. Then you multiply the dividend by the reciprocal of the divisor. Finally you simplify.

1 1/2 ÷ 2 3/4
= 3/2 ÷ 11/4
= 3/2 x 4/11
= 12/22
= 6/11

The dividend and the divisor are changed into improper fractions. Next the division operation is changed to a multiplication operation and the numerator and the denominator switch in the divisor. Then you multiply the numerator by the numerator and the denominator by the denominator to get the numerator and the denominator of the quotient. 12/22 can be simplified to 6/11 by dividing both the numerator and the denominator by a scale factor of 2. Problem Solving Order of Operations Subtracting fractions is a bit more challenging than multiplying and dividing by fractions, but is very similar to adding with fractions.

Take the question 2/3 - 1/5 for example.

The first step when subtracting fractions is to see if the denominators are the same. In our example, the denominators are different, therefore we have to find the least common denominator. The easiest way to do this is by listing all the multiples of the two denominators until we find the least common multiple.

3: 3, 6, 9, 12, 15
5: 5, 10, 15

The least common multiple is 15, therefore, our new denominator is 15, but since we changed the denominators, we also have to change the numerators as well.


2/3 - 2/5 For the first fraction, you needed to multiply the denominator by 5 in order for the
=10/15 - 6/15 denominators to be the same. What you did to the bottom, you must do to the top as well.
The same thing also must be done to the other fraction. Since we multiplied the
denominator by 3 to get 15, we also have to multiply the numerator by 3 as well.
Therefore the question is now 10/15 - 6/15.

Next, we subtract both numerators.

2/3 - 2/5
=10/15 - 6/15
=4/15 (Don't forget to box your answer!)

Since we can't simplify any further, 4/15 is our final answer.

Let's do another problem: 8/10 - 2/5

First, we check to see whether or not the denominators are the same. In this case, both denominators are different. Therefore we have to find the least common denominator.

10: 10
5: 5, 10
(10 is the least common factor, so 10 will be our new denominator).

Then, we subtract (don't forget to multiply 2 by 2 since you multiplied 5 by 2 to get 10):

8/10 - 2/5
=8/10 - 4/10
=4/10 Since both 4 and 10 can be divided by 2, it can be simplified to 2/5.
=2/5

When dealing with fractions, always simplify if you can. By Ayla, Ariane, Katelyn, and Lucia To solve an order of operations question you need to solve according to BERDMAS.

B - brackets
E - exponents
R - radical (square root)
D - division
M - multiplication
A - addition
S - subtraction

For example; (3/4 - 1/8) + 2/3 x 3/2 ÷ (2/1)²

According to BERDMAS, you first solve the expressions in the brackets.

(3/4 - 1/8) + 2/3 x 3/2 ÷ (2/1)²
= (6/8 - 1/8) + 2/3 x 3/2 ÷ (2/1)²
= 5/8 + 2/3 x 3/2 ÷ (2/1)²

Next you solve exponents or square roots.

5/8 + 2/3 x 3/2 ÷ (2/1)²
= 5/8 + 2/3 x 3/2 ÷ (2/1 x 2/1)
= 5/8 + 2/3 x 3/2 ÷ 4/1

Then you solve division or multiplication expressions according to the order they are in, therefore from left to right.

5/8 + 2/3 x 3/2 ÷ 4/1
= 5/8 + 6/6 ÷ 4/1
= 5/8 + 1/1 ÷ 4/1
= 5/8 + 1/1 x 1/4
= 5/8 + 1/4

Finally you solve addition and subtraction expressions according to the order they are in, therefore from left to right.

5/8 + 1/4
= 5/8 + 2/8
= 7/8

You break down the question according to BERDMAS and then you solve step by step. By Ayla, Ariane, Katelyn, Lucia By: Ariane To organize a problem solving question, you use the given, solve, statement format. In the given section, you write what you know about the question and you restate the question. In the solve section, you solve the question. In the statement section, you state your answer and check if the answer is reasonable.

For example; Seven people are sharing a cake. Michael wants one quarter of the cake, and Jessica wants one eight of the cake. What fraction of the cake can the other five people have if they split the remainder of the cake evenly between themselves?

Given:
One cake is being shared by seven people.
Michael wants a quarter of the cake.
Jessica wants an eight of the cake.

If the other five people split the cake evenly, what fraction of the cake can each person have?

In the given section we state what we know. We know the amount of cake Michael and Jessica want, so then we restate the question.

Solve:
[1 - (1/4 + 1/8)] ÷ 5
= [1 - (2/8 + 1/8)] ÷ 5
= (1 - 3/8) ÷ 5
= (1/1 - 3/8) ÷ 5
= (8/8 - 3/8) ÷ 5
= 5/8 ÷ 5
= 5/8 ÷ 5/1
= 5/8 x 1/5
= 5/40
= 1/8

In the solve section we solve the question. We know the seven people are sharing one cake so from one we subtract the amount of cake Michael wants, so 1/4, and the amount of cake that Jessica wants, so 1/8. We subtract the sum of 1/4 and 1/8 from 1. We need to find a common denominator when adding, in this case it is 8. 1/4 = 2/8 because we multiply both the numerator and the denominator by 2. 1/8 already has a denominator of 8 so it stays the same. 2/8 + 1/8 = 3/8. 1 is equal to 8/8. 8/8 - 3/8 is 5/8. 5/8 of the cake is the amount the other 5 people can share, therefore we divide 5/8 by 5. We multiply the dividend by the reciprocal of the divisor. 5/8 x 1/5 = 5/40 which can be reduced to 1/8 by dividing both the numerator and the denominator by 5.

Statement:
The other 5 people can each have 1/8 of the cake.

This answer is reasonable.

In the statement section we state the answer. In this case the answer is: each of the five remaining people can have 1/8 of the cake. Then you state if the answer is reasonable and if not, the answer is probably incorrect so you fix it. In this case, the answer is reasonable. When dealing with fractions, there will be times when fractions will be needed to be converted into decimals or percentages. Doing this is much easier than adding, subtracting, multiplying on dividing with fractions.

Turning fractions into decimals:

To turn a fraction into a decimal, all you have to do is divide the numerator by the denominator. For example:

Turn 4/8 into a decimal:

Numerator: 4
Denominator: 8

= Numerator ÷ Denominator
= 4 ÷ 8
= 0.5

4/8 in decimal form is 0.5.

Turning decimals into fractions:

Now that you know how to turn decimals into fractions, you will have to know how to turn decimals into fractions.

Take the decimal 0.75 for example:

First, take the decimal and put it over 1.

= 0.75/1

Next, multiply both numerator and denominator by 10 for every number after the decimal.

= 0.75/1
= 0.75/1 x 100/100 (There are 2 numbers after the decimal, 10 x 10 = 100)
= 75/100

The last step is to simplify the answer. So:

= 0.75/1
= 0.75/1 x 100/100
= 75/100 (Both Numerator and Denominator can be divided by 5)
= 15/20 (Both Numerator and Denominator can still be divided by 5)
= 3/5

3/5 can not be reduced, therefore it is our final answer. By Ariane Converting Fractions into Percents and Percents into Fractions By Ariane Just like converting fractions into decimals and decimals into fractions, converting fractions into percents and converted percents into fractions is fairly easy. It is also very similar to converting fractions into decimals.

Converting fractions into percents:

Take the fraction 25/100 for example.

Since the denominator is already out of 100, (percents will always be __/100) 25 will be your final answer.

25/100
= 25%

But, if it was a fraction not out of 100, like: 25/75, then this is how you would convert it.

First, turn the fraction into a decimal by dividing the numerator by the denominator.

= 25/75
= O.33... (repeating)

Next, multiply the decimal by 100.

= 25/75
= 0.33... (repeating)
= 33.33... (repeating)
= 33% (Since .33 is not needed, you can round the answer to 33%)

Converting percents into fractions:

Converting percents into fractions is very easy. First put the percent over 100.

= 50/100

And then simplify:

= 50/100
= 1/2 ( Both numerator and denominator can be divided by 50)

Therefore, the answer is 1/2. Subtracting with Negative Fractions By Ariane Subtracting with negative fractions is the exact same thing as subtracting regular fractions. The only difference is that your answer will be negative.

Take this problem for example: 1/4 - 2/3

Just like subtracting fractions, find the least common denominator, and then then simplify.

4: 4, 8, (12)
3: 3, 6, 9, (12)

1/4 - 2/3
= 3/12 - 8/12
= -5/12

When dealing with negative fractions, only the numerator becomes a negative number. -5/12 con not be simplified any further, therefore [-5/12] is our final answer.

Here is another example:

4/10 - 3/2
= 4/10 - 15/10 (Least common denominator is 10)
= -11/10 (-11/10 can be turned into a mixed fraction)
= 1 -1/10

1 -1/10 is our final answer. By Ayla GCF (Greatest Common Factor):

The greatest whole number that divides into two or more whole numbers with no remainder.
Ex:

Find all the factors of each number
Circle the Common Factors
Choose the greatest of the factors in the small group

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16

1, 2, and 4 are the common factors. 4 being the Greatest Common Factor.

Common Factors:

We have worked out the factors of two numbers:

Factors of 10: 1, 2, 5, and 10.
Factors of 12: 1, 2, 3, 4, 6, and 12.

The common factors are those that are found in both lists:

10: 1, 2, 5, and 10
12: 1, 2, 3, 4, 6, and 12
The common factors of 10 and 12 are 1, and 2.
It is a common factor when it is a factor of two or more numbers. It is then ‘common to’ those numbers.

Why is all this useful?:

Using it to simplify fractions
Ex:

How could we simplify 10/12?
The common factors of 10 and 12 were 1, and 2. So the Greatest Common Factor is 2. So the largest number can divide both 10 and 12 evenly by is 2.

÷ 2

10/12 = 5/6

÷ 2

•The Greatest Common Factor of 10 and 12 is 2.
•So 10/12 can be simplified to 5/6. Greatest Common Factor By Ayla When adding fractions, you must have the same denominator, or you will be incorrect. First, you must make equivalent fractions. Find the least common denominator.

1/2 + 2/4 LCD - 2: 2, 4
= 2/4 +2/4 4: 4
= 4/4
= 1

1) Are the denominators the same? If they are not, you must find the least common denominator.

2/7 + 3/10

2) Find the multiples for the denominators. If there is a common denominator between the two numbers, use that number as the denominator.

7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
10: 10, 21, 31, 40, 50, 60, 70

3) Now that you have a lowest common multiple, make two equivalent fractions. (Use the new common denominator)

2/70 + 3/70

4) Count how many numbers you put to get to 70 for both denominators.

7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 (10)
10: 10, 21, 31, 40, 50, 60, 70 (7)

5) Multiply the numerator by the number of jumps it took to reach your common denominator.

2/7 (x 10/10)
+3/10 (x 7/7)
= 20/20 + 21/20

6) Only add your numerators, leave the denominators the same. The denominators show the many many parts the whole has been broken into.

= 41/70

7) Since 41/70 can not be simplified, it is your final answer. (Don't forget
to box it). By Ayla By Ariane By: Lucia, Ariane, Katelyn, and Ayla
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