Sometimes math seems challenging until you can see and make sense of what you are doing. You work with fractions all the time but you may not realize it. We will go over some principlesโfacts that are always trueโabout fractions, and the next time you work with them, you will recognize and know it.

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### The Whole Shebang

You already know what a whole is. A whole is not just your arms, legs or ears, but all of you. You are a whole being. If someone was baking a pizza and you were paying for it, you would buy the whole thing to take home and share.

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### Parts of the Whole

Letโs take that whole pizza home for your family who are waiting to eat. If you have four people in your family, you will probably cut the pizza into equal parts so everyone can have their own uniform or identical share.

So say you divide the whole pizza into four big slices. Each person will take one piece of the whole. They will each get part of the whole. In the four pieces cut, they will each take one. That can be converted to a fraction! One slice of the pizza is one of the four cut, so a person will be getting 1/4โone-fourthโof the pizza. Each of the four people would be getting a part, or one-fourth of the pizza, and then it would be gone. Written as a fraction, it is 1/4.

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### Invite More to Share

What if there are more people? Say two more people are visiting from out of town. You are now picking up a pizza and they will want a share, or part, of the whole too. With six folks now, you can cut the pizza into six pieces instead of fourโthatโs so everyone will get their own equal share of the whole. Six pieces and each person gets one slice or how much of the whole pie? Every hungry person will get 1/6โone sixthโof the pie.

Now consider this: The piece each person is getting is smaller than when there were just four of you, right? Yes, 1/4 of the pizza pie is bigger than getting 1/6 the pie.

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### Smaller Still

Say instead you cut the pizza into smaller pieces. How about cutting the whole pizza pie into 12 equal pieces? Each of five people takes one piece or 1/12 of the pie. Each piece is very small, much smaller than 1/6 of the pie or 1/4 of the pie. 5 of the 12 pieces or as a fraction 5/12 are gone. How many are left? 12 pieces minus 5 pizza slices equals 7 pieces left. Now 7 of 12 pieces pizza are left in your pie; that can be written as a fraction, too: 7/12.

Now what happens if a new guestโthe sixth personโeats two pieces? They will be getting two of the twelve pieces. In fractions that would look like this: 2/12. They are getting two-twelfths or 2/12. They are getting 1/12th more than the others are. How many pieces would be left if each of the other five people takes just one? (Answer: 2/12ths plus 5/12ths equal 7/12ths. Can the other five people have one more piece? Yes.) There are now 6 people total and each one is getting 2 pieces. The pie is gone! They have eaten 12 pieces or 12/12 = 1 whole pie.

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### Top and Bottom

Each fraction has a top number and a bottom number. The top number is called the numerator. The bottom number is called the denominator. In the first pizza pie example, the first time we cut the pizza we cut it into four pieces of the whole, the top numerator is 4 and the bottom number, or denominator, is 4 also. 4/4.

Now when one piece is taken, the top numerator is one piece and the bottom denominator is 4. 1/4 of the pie is taken. If another person takes their equal piece, another 1/4 is gone, so the top numerator would be 2 and the denominator is still 4. Two pieces of the four pieces taken as a fraction is 2/4. This means that two pieces of the four pieces are gone.

How will the fraction look if a third person takes their piece now? Three people have taken one of the four pieces so the fraction would look like 3/4. How many slices are left over now? Just one or 1/4. One (1) is the numerator and four (4) is the denominator. The numerator rides over the denominator.

The larger the top number of a fraction, the larger the numerator. The fraction is larger when the denominator or bottom number stays the same.

Now if the larger number is the denominator, on the bottomโthe smaller the fraction when the numerator or top number is the same. 1/12 is larger than 1/15.

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### Fractions are Everywhere

Later on, you will learn to add fractions, subtract fractions, multiply fractions and express the same fractions using smaller numbers.

Fractions are part of a mathematic principle, which means that fractions are in your life. Fractions are in pizza slices, in money, in time, in percentages and everywhere.

For example:

1/4 of the football game is a quarter, and it is also 15 minutes long or one-fourth of an hour.

School shirts are on sale and they are 1/2 off! This means they are 50 percent less than they were before the sale.

The babyโs shoes were a size 3 but now they are a size 3 ยฝ. They are size 3 but also add in another ยฝ size that makes them just a half size as big as before, yet they are still less than size 4.

You see fractions will become a part of your life, so enjoy working with them and you too, will become a whizz at mathematical fractions.

### References

- Birmingham Grid for Learning: Beginning Fraction Tutorial
- Kids Online Resources: Continued Fraction Game
- Adler, David A. Working with Fractions. New York: Holiday House, 2007. Book.
- EdHelper: Illustrations for Education