The person below suffers from Fraction Phobia. Do you?

Understanding fractions while eating pizza>

~In my opinion, slicing & eating pizza is an excellent way to understand
 the meaning of fractions.

~All numbers are fractions. Whole numbers are fractions with bottoms  (denominators) of one. (usually not written)

~Tops (numerators) can be smaller than the bottoms (proper fractions) or  larger than the bottoms (improper fractions)(not for negatives).

~The number in the bottom (denominator) gives the number of identical  slices of your pizza pie (before you & your friends indulge).

~The number in the top (numerator) corresponds to the number of identical  slices about to be eaten.

~If you wish to understand 8 ths, slice your pizza pie in 8 identical slices, for 16 ths, 16 identical slices, for 5 ths, 5 identical slices, & so on. You  have the freedom to slice it into as many identical slices as you wish.

~For improper fractions (top bigger than bottom), you need more than one  pizza pie. For example, 8/5 means you are to eat 8 identical slices but  your pie has only 5. So, you need another identical pizza pie sliced up in 5 slices so that you can eat 3 more. Total eaten here would be one  whole pie plus 3 slices out of 5 from the 2nd pie. The 2nd pie still has 2  slices left.

Adding pizza slices

~Adding fractions is like adding pizza slices. However, there is a rule in  human nature that says you can't eat different size slices, they must all  be identical. A problem lies with pies that are sliced in different numbers of  slices, since some slices will be smaller or larger than other slices. So,  how does one make all the slices the same shape? Necessary before  adding?

~Let's say you want to add 3/8 and 5/24. You might be able to do this with  one pizza pie, if there is enough. You cannot slice a pie into slices more  than once, so be careful the first time. For these two fractions, one person  wants 8 identical slices but another person wants the same pie sliced into  24 identical slices. You need to satisfy both. Look at the bottoms & figure  the number of slices that will be the LCM (least common multiple). This LCM  is a number that contains all factors of 8 & 24 exactly once. (smallest  number that is exactly divisible by both 8 & 24). It is 24. So, slice your pie  into 24 identical slices. The 8, in the first fraction, is now 24. If you change  the bottom, the top must be changed also. Since 8 was multiplied by 3 to  get 24, you need to multiply the top by 3 also, to get 9. So, the first fraction  is now 9/24. Now the pizza pie can be sliced into 24 identical slices & you  can add them. 3/8 becomes 9/24 (eat 9) & for 5/24 (eat 5 more) for a total  of 14 out of the 24 slices (14/24). That leaves a lot of pizza slices left in that  pie.

~The LCM is know as the LCD (lowest common denominator).

~Since subtraction is just adding a negative, think of subtracting slices as taking  them away from the person who is about to eat them & putting them back  into the pie. For example,  4/5 minus 3/7. Here again, the numbers in  the bottoms indicated different size slices..a no-no. We need to find the LCM  of 5 & 7. Since they do not share any factors, it will be their product, 35.  So, the pie is sliced into 35 identical slices. The 4/5 becomes 28/35 and  the 3/7 becomes 15/35. For our subtraction problem, the first person takes  4/5 of the pie or 28 out of the 35 slices. But you take from the person 15 of  those slices & put them back into the pie. So, the person will only eat  28-15 or 13 slices out of the 35 (13/35). This is the answer to the subtraction.

Multiplying & dividing

~It's easier to multiply & divide fractions compared to adding & subtracting them.  Just know the rules.

~For multiplying, Tops times Tops & bottoms times bottoms.  For example, (5/7)(7/2)=35/14. You can reduce (equivalent fraction with  smaller numbers) this to 5/2. Notice that if you cross out any number from  the bottom with the same factor in any of the tops, its OK. For (5/7)(7/2) we  can cross out the 7's & get our answer quickly & not have to reduce. This  can save us a lot of time. Here's another example: (11/19)(3/8)(19/5)(8/11)  equals 3/5. Note that the 11's, 8's, & 19's can be crossed out.

~The rule for dividing Two fractions is also simple. Just flip the fraction you are  dividing by and change the operation to multiplication. Then follow the rules  above. For example,  7/8 divided by 49/24 = (7/8)(24/49). Now notice that 24  contains a factor of 8 ( 3 times 8), so the 8 divides the 24 & leaves a 3.  Likewise, with the 7 & 49, the 7 divides into the 49 & leaves a 7 (in the bottom).  Remember, you can only do this with two numbers (one of which is in the top  & the other in the bottom). So, our problem becomes (1/1)(3/7)= 3/7.

~Here is a useful short-cut for dividing a fraction by a number (or quantity in  higher math). Try to divide the top by the number (quantity). If it does, just  write the answer over the original bottom. For example, 210/73 divided by 7.  Since 7 divides the top, 210, do it. The answer is 30/73.  If the number does not divide the top, just multiply the bottom & write the  answer. For example,  29/63 divided by 7. Since 7 does not divide 29, just  multiply the bottom & write the answer, 29/441.

~When working with mixed numbers, such as 3 & 8/11, convert all of them  to fractions (since all numbers are fractions) & use the rules above.
 For example,  (3 & 9/11)(2 & 5/6) = (42/11)(17/6) = (7/11)(17/1)=119/11  Note that the 6 in the bottom divides the 42 in the top & leaves a 7 (in the  top).

~When working with complex fractions (tops and/or bottoms contain fractions)  change the top & bottom to single fractions & use the division rule.  For example, [(1/3)+(3/5)] divided by [(7/8)+(1/4)] = [(5/15)+(9/15)] divided  by [(7/8)+(2/8)] = (14/15) divided by (9/8) = (14/15)(8/9) = 112/135.  Notice that no factors are common to the numbers of the tops & bottoms.  So, when you write the final answer, it is already reduced.

~Comparing the value of fractions (which is larger or smaller) is also very  easy to do. Just use a calculator (or long division) & take the top & divide  it by the bottom, this gives the decimal equivalent. Just look at it & you'll  see which one is bigger. For example, compare 37/83 & 56/123. The  decimal equivalent of the first is .446 (3 places), the decimal equivalent of  the 2nd is .455, so the 2nd is slightly bigger.

~Also, if two fractions have the same bottom, the one with the bigger top is  larger. Similarly, if two fractions have the same top, the one with the smaller  bottom is larger. (not true for negative numbers, however). They have their  own set of rules.

~Be extra careful with negative numbers. Any negative number is smaller than  any positive number. Also, larger negative numbers are smaller than small  negative numbers. For example,  -3,000 is much smaller than -.001. Think  of the x axis & the position of the number. A number to the right of another  number is larger. So, -.001 is way to the right of -3,000 on the x axis, so it  is much larger.

~There are several different approaches to explaining fractions, this is just one.  I find it the best for people who have fraction phobia.

Hope you enjoyed this little pizza trip. I'm hungry...for pizza.