Fractions Introduction

How to add Fractions

Examples of Like Denominator Adding

3/5 + 1/5: In this you just have to add the numerators, which is 3+1. The answer is 4, so just put the denominator on, and you're done! So, the answer is 4/5.

Examples of Unlike Denominator Adding

5/6+7/9: In this you have to do cross multiplication. The first fraction is 5/6, so we have to multiply it by a form of 1, and since the other fractions denominator is 9, we will multiply it by 9/9. You get 45/54. We do the same to 7/9, but multiply it by 6/6, and we get 42/54. Then we add them and get 87/54. If you simplify it, you get 1 33/54, and you simplify it one more time, you get 1 11/18.

There are 2 parts to a fraction.The numerator and the denominator. The numerator is the top part of a fraction like the 1 in 1 fourth. The denominator is the bottom part of a fraction like the 4 in one fourth. Usually, fractions are in the range of 0 and 1, except for a mixed number or improper fraction. We are going to explain that in frames 8 and 9.

Fractions!

Like Denominators

Unlike Denominators

Adding fractions with like denominators is simple: just add the numerators, and leave the denominators alone.

In adding unlike denominators, you have to make them like denominators. You have to do cross multiplication, or the butterfly method. We will go over that in slide 12 and beyond. After you get them to the same denominator, you do the steps of adding like denominators.

How to Reduce Fractions

Reducing fractions is finding easier numbers to work with, or finding equivalent fractions. Like if you take 6/8 of a pizza, it is the same as 3/4. First, you find the GCF, or greatest common factor. That is mentioned in slide 11. Then, you divide the fraction by the GCF. In 3/6, the GCF is 3, so you divide 3 by 3 and get 1. You divide 6 by 3 and get 2. So your final answer is 1/2.

Mixed Numbers are a fraction with a whole number, like this: 1 1/3. Mixed numbers in the real world are like this: 1 3/8 pizzas, 2 7/8 liters of soda, etc. It really means 1 whole pizza and 3/8 of another one, or 2 whole liters of soda and 7/8 of another one. Mixed numbers also come into play while reducing improper fractions, such as 7/3 being reduced to 2 1/3. Mixed numbers can also be converted in to an improper fraction by following these steps: Multiply the denominator by the whole number and add the numerator to the sum, and keep the denominator the same. Like this: If the fraction is 2 1/3, I multiply 2 by 3 and get six, and then add 1 to six and get seven. So my final answer is 7/3.

Improper Fractions

Improper fractions are fractions who's numerators are larger than their denominators, like this: 7/3. Improper fractions can be reduced to mixed numbers by just dividing the numerator by the denominator. So, in 7/3, I would divide 7 by 3 and get 2R1. The remainder becomes the numerator of your fraction part of the mixed number, and the quotient becomes the whole number. So I would get 2 1/3 as my simplified fraction. In some cases, when you reduce it, the fraction part of the mixed number can still be reduced. Like this: 2 2/6. I just reduce the fractional part like I would normally.

LCM (least common multiple)

LCM is used when adding fractions with unlike denominators. Take 5/6 and 7/9. What do you do? You find the LCM, or Least Common Multiple. First, you list the multiples of 6 and 9, including 6 and 9.

6: 6, 12, 18

9: 9, 18.

The first common multiple we found was 18, so we multiply the fractions (numerator

and

denominator) so that the denominator will be 18. For 5/6, we multiply it by 3, so we get 15/18. For 7/9, we multiply it by 2, so we get 14/18. Then we add. 15/18+14/18 is 29/18. We simplify it and get 1 5/9.

GCF (greatest common factor)

GCF is used when reducing fractions. (see panel #4) When using it, you have to list all the factors of the numerator and the denominator. Take 33/54. First, we list the factors of 33:

1,3,11,33

Now list the factors of 54:

1,2,3,6,9,18,27,54.

Now we find the greatest factor that they have in common, which is 3. So we divide the numerator and the denominator by 3. We get 11/18. The way we know that the fraction is fully reduced is that the only factor that they have in common is 1.

Fractions are a pivotal point in mathematics. It is one of the main ways to show an unit below zero, or a unit slightly above a whole number. Fractions have many sides, but we'll go over those later. Lets get to basics. The parts of a fraction are a denominator, the bottom number and a numerator, the top. Follow this link to learn more. Click here

https://www.khanacademy.org/math/arithmetic/fraction-arithmetic

The rest will be taught in this informative Prezi!

There are many methods to add, subtract, multiply, and divide fractions. I will be going over the butterfly method (aka moth man of doom method) C/mad method finding a common denominator, and more.

Butterfly Method

The butterfly method is when you cross multiply the numerators and denominators of the fractions. You multiply the denominators together. Then you add or subtract the numbers you got before. This Khan Academy video will provide more information:

http://www.moveitmaththesource.com/realfractions/butterflyfractio.html

Methods!!!

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This method is where you make mixed numbers into improper fractions. First you multiply the whole number by the denominator. Next you add the numerator. Put the number you got on top of the same denominator as the last number. You can use this method when you are trying to use mixed numbers in the butterfly method.

The C Method

You can find equivalent fractions by multiplying both the numerator and denominator by the same number. Same works with dividing.

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Finding Equivalent Fractions

Word Problems

If Jeff ate 3/4 lbs. of bacon and Piggelz ate 7/5 lbs. of bacon, how many lbs. of bacon did they eat?

If Bob drank 2/3 a liter of coconut water, and his son drank 8/9 of a liter, how many more liters did Bob drink than his son?

Mrs. Lucas made 10 5/6 cakes on Monday, and Mrs. Telesz made 7 and 8/9 cakes on Tuesday, and Mr. Ortega made 7/10 of a cake on Wednesday, and Mr. Stevens made the amount of all them combined, then how many cakes did Mr. Stevens bake?

Manas beat 7 2/3 video games. Brendan beat 5 1/7 video games. How many more video games did Manas beat then Brendan?

Samesh ate 2 1/6 kg. of rice. His dad ate 5 8/9 kg. of rice. How many kilograms of rice did they eat together?

Mixed Numbers

http://www.mathgoodies.com/lessons/fractions/equivalent.html

www.mathsisfun.com/fractions_addition.html

Here's a little help:

http://www.purplemath.com/modules/lcm_gcf.htm

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