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jessica sum

on 31 January 2013

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Transcript of math

by Jessica Fractions The basics Adding and Subtracting Fractions Adding the numerator is the easy part. The denominator is the hard part. How to convert fractions to decimals and vice versa Converting fractions to decimals is simple. Multiplying and dividing fractions For multiplying and dividing, you will need to simplify. Converting fractions to percentage and vice versa Converting fractions to percents is easy To start off, we need to
know what a fraction is. A fraction is a numerical quantity which is not a whole number. This is a fraction. This is not. Parts of a fraction 1. 2. 3. 1. the numerator
the numerator is the top part of any fraction 2. the denominator
the denominator is the bottom part of any fraction 3. the fraction bar
the fraction bar is the bar in the middle of the numerator and the denominator. it is a part of every fraction. Types of fractions There are three types of fractions: proper fractions, mixed fractions and improper fractions A mixed fraction is when a whole number and a fraction are combined. An improper fraction is when the numerator is greater than or equal to the denominator. If you do not want the numerator to be greater, you would need to change the fraction into a mixed fraction. A proper fraction is when the denominator is greater than the numerator. Next, learning how to simplify a fraction is essential. For this, you will need to be good in division, or else, this part will be hard. How to simplify Simplifying fractions means making them into the simplest form. To simplify, find a common factor between the numerator and denominator. For example, in the example, the first fraction 3/6 was divided by three because that was the common factor between 3 and 6. the answer is 1/2. which comes down to the next lesson: greatest common factor. GCF=Greatest Common Factor What is a factor? Factors are numbers you can multiply together to get another number. What is a common factor? Example: Factors of 6 and 12: The common factors are the factors that are found in both lists of factors highlighted in blue like 1, 2, 3. What is the greatest common factor? The greatest common factor is basically the largest common factor. Like the last example, there was more than one. But the greatest common factor is the largest. 6: 1, 2, 3, 6 12: 1, 2, 3, 4, 6, 12 In this case, it's 6. Last is equivalent fractions Equivalent fractions have the same value. The only difference is that the numerator and denominator are in a simpler form. Since the denominator is different, you cannot add it. therefore, you have to find the LCM. LCM=Lowest Common Multiple What is a multiple? The product of two numbers, one of which is always the same. What is a common multiple? In this example, the number that always stays the same is three. Example: Multiples of 2 and 4: 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ... The common multiples are the numbers that are in both lists of multiples highlighted in blue. What is the lowest common multiple? Basically, it is the smallest multiple. For the previous example, there were many common multiples. but only the number with the least value will be the lowest common multiple. In this case, it is 4. Example: In this case, the denominators are different. So, you have to find the LCM. multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, .... multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,.... The common multiple between 8 and 4 is 8. So, you have to multiply the fractions in order to have the denominator at 8. 3/8 =3/8 6/4=12/8 3/8 +12/8=15/8 You will notice that I only added the numerator. You DON'T add the denominators together. Since the answer is an improper fraction, it is not the final answer. The final answer is 1 7/8. Subtraction is the same as addition, but you have to subtract, not add. The first part of doing subtracting fractions is the same as adding fractions. If the denominators are different, you have to find the LCM. example: a few notes:
-the denominators are different, so, we have to find the LCM multiples of 3: 3, 6, 9, 12, 15, 18, 21, ... multiples of 5: 5, 10, 15, 20, 25, 30, 35, ... LCM: 15 1/3 = 5/15 2/5 = 6/15 5/15 - 6/15 = 1/15 Note again that I did not subtract the denominator. Multiplication: In multiplication, you can simplify a denominator and a numerator. You CANNOT simplify a numerator and a numerator or a denominator and a denominator. GCF of 4 and 32:
4: 1, 2, 4
32: 1, 2, 4, 8, 16, 32 The GCF of 4 and 32 is 4. 4 divided by 4 equals 1
32 divided by 4 equals 8 There is no common factor. So there is no way to simplify the fractions. Result: after you simplified all you can, for the numerators, you will end up with 24 times 1. for the denominators, you will end up with 8 times 7.
24 times 1 equals 24
8 times 7 equals 57 Final result: 24 over 57 Finally, you can still simplify the answer. If they have a common factor, you can. There is still a common factor.
24 divided by 3 equals 8
57 divided by 3 equals 19 Final answer after simplifying: 8 over 19 Dividing fractions is a little trickier. GCF of 7 and 24
7: 1, 7
24: 1, 2, 3, 4, 6, 8, 12, 24 GCF of 24 and 57
24: 1, 2, 3, 4, 6, 8, 12, 24
57: 1, 3, 19, 57 Division: You may have noticed that after the equal sign, in the second fraction, the numerator and denominators switched places, the reason being, there is no way to divide fraction like that. After you flip the second fraction, you can just multiply like normally. But there is one condition of flipping the second fraction. In order to do that, you have to switch the divide sign to a multiplication sign. Then the tricky part comes. You cannot flip the first fraction. You have to flip the second fraction. Simply use a calculator. To find the decimal, divide the numerator by the denominator. Example: 2 divided by 5 equals 0.4 MUST REMEMBER 1 over 2 = half = 0.5
1 over 4 = 0.25
3 over 4 = 0.75
1 over 5 = 0.2
2 over 5 = 0.4
3 over 5 = 0.6
4 over 5 = 0.8 Converting decimals to fractions is a bit harder. First, put the decimal over 1. Then, find out how many digits there are after the decimal. If there is one zero, divide the numerator and denominator by 10. follow this chart:
1 digit-multiply by 10
2 digits-multiply by 100
3 digits-multiply by 1000 After, you multiply, simplify if it's possible. Like when we converted fractions to decimals, the simplest way to do this is to use a calculator. Change a number that can change the denominator to 100. It can be a whole number or a decimal. After you found the number, just multiply the numerator and denominator by that number. There you go! You found the percent! Finally, put a percent sign beside the numerator, take out the fraction bar and denominator and ...... Converting percentages to fractions is super easy. Simply take out the percent sign, put a fraction bar and a denominator of 100. Just make sure that the denominator is 100. After that if you can simplify, do that. Then, you're done! On this prezi, you have learned:
-what is a fraction
-how to simplify a fraction
-GCF and LCM
-what are equivalent fractions
-how to add and subtract fractions
-how to multiply and divide fractions
-converting fractions to decimals and vice versa
-converting fractions to percentages and vice versa THE END!!!!!!!!!!
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