Reading and Writing Fractions

As most parents know, a fraction is a way of expressing parts per whole. A whole number can be divided into as many parts as you want and as long as you have all the parts, the number can be represented as 1. Say, for example, your child has a pizza with ten slices. The whole pizza can be represented as 1 or as 10/10, meaning he has ten out of ten parts.

 Once he starts sharing his pizza with his friends, he shows what’s left by writing it as the number of slices left (the part) over the number he started with (the whole).

If he’s eaten two slices of pizza, he’s eaten 2/10--two tenths--of the pizza and has 6/10 left. The bottom number, or the denominator, is always all the pieces and the top number, the numerator, is always the number of pieces.

 The Golden Rules of Fractions

1. If you do something to the numerator, you must do the same thing to the denominator.  

2.  Any number over itself is equal to 1.   

 Types of Fractions

• Equivalent Fractions: Equivalent fractions may look different but equal the same amount. For instance, 5/10 is equivalent to ½ because if you divide both the numerator and denominator of 5/10 by 5, you get ½. Likewise, multiplying the numerator and denomination of 1/2 by 5 gives you 5/10.

• Proper Fractions: A proper fraction has a numerator that is smaller than the denominator.

• Improper Fractions: Improper fractions are sometimes referred to as “top heavy.” This means the numerator is larger than or equal to the denominator. In this case, the fraction is equal to more than just a few parts of the whole, it’s equal to one whole and some more parts. For example, 3/2 is the same as 2/2 + 1/2, or, 1 + 1/2.

• Mixed Number Fractions: A mixed number fraction is what you get when you correct an improper fraction. It’s a whole number combined with a proper fraction.

 Reducing Fractions

Reducing fractions is also known as simplifying. It means making a fraction as small as it can possibly be, essentially making it the smallest of equivalent fractions. There are a couple of ways to reduce fractions.

1. Divide the numerator and denominator over and over.  If you have a fraction like 25/150, it is obvious that the number 5 divides into both the numerator and denominator. You can divide by that obvious number over and over, until you can’t divide anymore. Example: 25/150 ÷ 5 = 5/30. Divide again and 5/30 ÷ 5 = 1/6. It cannot be divided again. 
2. Use the greatest common factor. The greatest common factor is the largest number that will divide evenly into two or more numbers. In the previous example, the greatest common factor for 25 and 100 is 25. So, 25/150 ÷ 25 = 1/6.
   

Adding and Subtracting Fractions

Adding and subtracting fractions won’t be as easy for your child as adding and subtracting whole numbers. Those fractions need to be expressed as parts of the same whole before they can be added. Otherwise, it would be like trying to combine slices of cake with slices of pizza; it won’t work.

Step 1: Find a common denominator. If the denominators aren’t the same, your child will have to find a number that is a factor of both denominators. It’s helpful if it’s the smallest number that both will divide into, but he can also multiply the denominators together to get that number. For example, in the fractions ½ and ¾, both denominators are will divide into 4, making it the lowest common factor.

Step 2: Make equivalent fractions. Your child will need to write both fractions with the common denominator. Since ¾  already has the correct denominator, it doesn’t need to be changed. However, ½ needs to multiplied by 2/2 (remember the golden rule!) to become 2/4.

Step 3:  Perform the operation. If the problem was 1/2 +3/4 , it has become 2/4 + 3/4 which equals 5/4. If the problem was 3/4 - 1/2, it becomes 3/4 - 2/4 which equals 1/4.

Step 4:  Reduce the fraction. In some cases, the answer will be as small as it can be, as it is with 1/4. In other cases, the fraction can be made smaller, as it is with 5/4, which is equal to 1 1/4.

Multiplying Fractions 

Multiplying fractions is easy. All your child has to do is multiply the numerators together and the denominators together. The answer is: (numerator A x numerator B) over (denominator A  x  denominator B).  Example: 1/4 x 3/5 = 3/20

Dividing Fractions 

Dividing fractions is just as easy as multiplying. Simply flip the fraction you are dividing by upside down and then multiply. Example:  1/6  ÷ 3/6 = 1/6 x 6/3. The answer is 6/18, which can be reduced to 1/3.