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  1. 1. Fractions <ul><li>By. Maxx Kim </li></ul>
  2. 2. <ul><li>A fraction is a numerical quantity that is not a whole number. Such as 1/2, or 1/5. 3/10. </li></ul>What is a Fraction?
  3. 3. <ul><li>The most important part in a fraction is that it has a numerator and a denominator. </li></ul><ul><li>Example. 1  Numerator </li></ul><ul><li>2  Denominator </li></ul><ul><li>The top part is the numerator ( 1 ) </li></ul><ul><li>the bottom part is the denominator ( 2 ) </li></ul>Parts of a Fraction
  4. 4. <ul><li>Okay so now that you know all the parts to a fraction first lets learn how to multiply fractions </li></ul><ul><li>In order to do that here’s an example </li></ul><ul><li>1 X 4 </li></ul><ul><li>2 7 </li></ul><ul><li>So in order to do this all you have to do is multiply the numerators and denominators together. If you do it yourself you should get 4/14 </li></ul>Multiplying Fractions
  5. 5. <ul><li>Dividing fractions is easy! It's very very similar to multiplying except it has one extra step. </li></ul><ul><li>So as an example lets use the last problem we did to make things easy. </li></ul><ul><li>1 4 </li></ul><ul><li>2 7 </li></ul><ul><li>Step 1 Flip the 2nd fraction so that the numerator is now the denominator, and the denominator is the numerator </li></ul><ul><li>1 7 </li></ul><ul><li>2 4 </li></ul><ul><li>Step 2 </li></ul><ul><li>Turn the division sign into a multiplication sign </li></ul><ul><li>1 X 7 </li></ul><ul><li>2 4 </li></ul><ul><li>Step 3 Solve </li></ul><ul><li>If you do these steps you should get 7/8 </li></ul>Dividing Fractions
  6. 6. <ul><li>For Adding and subtracting fractions the first step you have to do is trying to find something called the least common denominator, also known as LCD. </li></ul><ul><li>To find the least common denominator, simply list the multiples of each denominator (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. </li></ul>Adding Fractions
  7. 7. <ul><li>Example: Suppose we wanted to add 1/5 + 1/6. We would find the least common denominator as follows. </li></ul><ul><li>First we list the multiples of each denominator. </li></ul><ul><li>Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,... </li></ul><ul><li>Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,... </li></ul>Adding Fraction cont.
  8. 8. <ul><li>Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list </li></ul><ul><li>Therefore, the least common denominator of 1/5, 1/6 is 30 </li></ul><ul><li>so now that we found the LCD there’s also another rule that follows up which is, “what you do to the bottom you do to the top.” For the first fraction 1/5 and the common denominator is 30 so that means you multiplied 5, 6 times in order to get 30. So you also multiply 6 to the top number to. Giving you 6/30. </li></ul><ul><li>Lets do the same for 1/6. The LCD was 30, so you multiplied 6, 5 times in order to get 30. And you also multiply that by the top giving you 5/30. </li></ul><ul><li>So far this is what we have so far. </li></ul><ul><li>6 + 5 </li></ul><ul><li>30 30 </li></ul><ul><li>when you get here all you have to do now is add the numerators together but just carry over the 30. (DO NOT TOUCH THE DENOMINATOR!) Giving you 11/30 which is the answer. </li></ul>L.C.D
  9. 9. <ul><li>Subtracting fractions is almost the same as addition. Lets use the same problem in adding fractions. </li></ul><ul><li>1 - 1 </li></ul><ul><li>5 6 </li></ul><ul><li>Step 1 so again you find the common denominator which was 30 right? </li></ul><ul><li>6 - 5 </li></ul><ul><li>30 30 </li></ul><ul><li>Step 2 you then just subtract only the numerators again and just carry over the denominator which gives you 1/30. </li></ul>Subtracting Fractions
  10. 10. <ul><li>So basically this time I’m going to show you how to do fractions using variables. This makes things a little more trickier because instead of dealing with numbers were dealing with letters. Don’t let them confuse you though. Here’s the </li></ul><ul><li>X+3 - x </li></ul><ul><li>X-1 x+1 </li></ul><ul><li>  </li></ul>Fractions w/varibles
  11. 11. <ul><li>Ok so Step 1 just like any other subtraction fraction problem you have to find the LCD. Except this time finding it is a bit different. </li></ul><ul><li>To find the Common Denominator this time look at this formula </li></ul><ul><li>a*b=b*a </li></ul><ul><li>so knowing this take a look at what I’ve done so far. </li></ul><ul><li>(x+3) (x+1) - x(x-1) </li></ul><ul><li>(x-1) (x+1) (x+1) (x-1) </li></ul>Fractions w/Varibles cont.
  12. 12. <ul><li>If you noticed I added a few numbers to the equation making it look confusing. </li></ul><ul><li>So to find the denominator I multiplied </li></ul><ul><li>“a” by “b”, and “b” by “a” using a FOIL method. </li></ul><ul><li>a=x-1 </li></ul><ul><li>b=x+1 </li></ul><ul><li>Also don’t forget the rule where what you do to the top you do to the bottom. </li></ul><ul><li>(x+3) (x+1) - x(x-1) </li></ul><ul><li>(x-1) (x+1) (x+1) (x-1) </li></ul>Fractions w/Varibles cont.
  13. 13. <ul><li>So now that you know that if you do FOIL you get this </li></ul><ul><li>x2 +x+3x+3 - x2 -x </li></ul><ul><li>x2 +x-x-1 x2 -x+x-1 </li></ul><ul><li>Here I just combined like terms. </li></ul><ul><li>x2 +4x+3 - x2 +x </li></ul><ul><li>x2 -1 x2 -1 </li></ul>Fractions w/Varibles cont.
  14. 14. <ul><li>x2 +4x+3 – x2 + x </li></ul><ul><li>x 2-1 x 2-1 </li></ul><ul><li>Now all you do is subtract the Numerators up top. </li></ul><ul><li>So if you do that you get the answer at the bottom. Again you just carry over the common denominator. (DO NOT SUBTRACT THE DENOMINATORS!) </li></ul><ul><li>5x+3 </li></ul><ul><li>x 2 -1 </li></ul>Fractions w/Varibles cont.