Fractions
Definition of a Fraction 
This image shows the parts of the fraction: The numerator and the denominator. Source: Matthew Pugh, 2008
A fraction is just another way to write a division problem.  is just another way of saying  since the line of a fraction means "divided by." Fractions are mainly just a different way of writing decimals down as it is sometimes easier to understand and write fractions then the actual decimal equivalent.
 for instance could also be written as the decimal 0.0588235294..., but the fraction is a lot less to write down!
Resoures
Games: [PBS Fraction Matcher] - Match fractions with picture equivalents.
Conversion
Changing a Fraction to a Decimal
To change a fraction to a decimal, all you need to do is to take the top number and divide by the bottom number. For instance ¼ can be found on a calculator by taking 1 and dividing it by 4.
Changing a Mixed Number into a Decimal
To change a mixed number into a decimal, you do roughly the same as changing a fraction into a decimal. First, you start with the fraction and change it into a decimal. Next, you add on the whole number in front of the mixed number to get your final answer.
For example, 5½ can be changed to a decimal using a calculator by first changing the fraction part: 1 divided by 2 = 0.5. Next, take your answer and add to it the whole number. In this case it is 5. 0.5 + 5 = 5.5. 5.5 is the final answer.
Equivalent Fractions 
This shows how to make an equivalent fraction. Source: Matthew Pugh, 2008
An equivalent fraction is a fraction that works out to be the same as another, but using different numbers. For instance one half is the same as two quarters.
Improper fractions
An improper fraction is a fraction where the top number is larger than the bottom one. In Mathematics, this is not recommended. You should use mixed numbers instead.
Mixed Number
A mixed number contains one part regular number, and one part fraction. 1½ is an example of a mixed number. 1 is the number part, and ½ is the fraction part.
Resources
Books
- Transition Mathematics p50-52
Videos
- [Mr. Duey's Fraction Rap] - A youtube video all about converting between improper fractions and mixed numbers as well as turning fractions into percentages.
Games
Operations
Addition and Subtraction
You can't just add and subtract fractions easily. We know, for instance, that a half plus a half is equal to one, right? To add fractions, first the bottom number must be the same. Then, we can add or subtract the top number.
If the bottom numbers of a fraction are not the same, then you need to make them the same. One way to do this is to change one fraction into an equivalent one.
 
In the above example, I changed  into  by doubling both the top and the bottom numbers. This is the easiest way to find a common denominator. Now that both bottom numbers are the same, I can just add the top numbers and get an answer.
Resources
Books
- Transition Mathematics p260-265 - positive and negative fractions
- Transition Mathematics p266-268 - Relating to probabilities
Videos
Games
Multiplication
Multiplying fractions is much easier than adding or subtracting. To multiply a fraction, simply think of it as two multiplication problems in one.
Think of this as two problems:
- The top numbers of the fractions multiplied together
- the bottom numbers of the fractions multiplied together
Once you have your answers, put them together in the form of a new fraction:  After this, reduce the fraction to simplest form if required.
Resources
Videos
Games
Division
Division isn't too much more difficult than multiplication. There are many ways to divide fractions, but often times the simplest way is to flip the second fraction upside down, and then treat it like a multiplication problem.
 ÷ 
If you flip the second fraction upside down, you get: 
Resources
Videos
Games
Back to Mr. Pugh's 7th grade math page
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