a = numerator

b = denominator

Examples of prime numbers are 2, 3, 5, 7, 11, and 13.  The list can go on and on. 

Be careful, 1 is not a prime number because it only has one distinct factor which is 1. 

When you rewrite a number using prime factorization, you write that number as a product of prime numbers.

For example, the prime factorization of 12 would be 

That last product is 12 and is made up of all prime numbers.

Step 2: Use the Fundamental Principle of Fractions to cancel out the common factors.
 

Make sure that you do reduce your answers, as shown above.  You may do this before you multiply or after.

*Div. the common factor of 5 out of both num. and den.

In other words, you flip the number upside down.  The numerator becomes the denominator and vice versa. 

For example,  5 (which can be written as 5/1) and 1/5 are reciprocals.  3/4 and 4/3 are also reciprocals of each other.

*Write as prod. of num. over prod. of den.

*Div. the common factor of 2 out of both num. and den.

Step 2: Put the sum or difference found in step 1 over the common denominator.
 

Step 3: Reduce to lowest terms if necessary.
 
 

Why do we have to have a common denominator when we add or subtract fractions?????
Another good question.  The denominator indicates what type of fraction that you have and the numerator is counting up how many of that type you have.  You can only directly combine fractions that are of the same type (have the same denominator).  For example if 2 was my denominator, I would be counting up how many halves I had, if 3 was my denominator, I would be counting up how many thirds I had.  But, I would not be able to add a fraction with a denominator of 2 directly with a fraction that had a denominator of 3 because they are not the same type of fraction.  I would have to find a common denominator first before I could combine, which we will cover after this example.

You can achieve this by multiplying the top and bottom by the same number.  This is like taking it times 1.  You can write 1 as any non zero number over itself.  For example 5/5 or 7/7.  1 is the identity number for multiplication.  In other words, when you multiply a number by 1, it keeps its identity or stays the same value. 

*Multiply num. and den. by 4.

An improper fraction is a fraction in which the numerator is larger than the denominator.

*Mult. den.  4 times whole number 7 and add it to num.  3.
 
 

*Improper fraction
 

Step 1: Find the Least Common Denominator (LCD) for all denominators. 
 

Step 2: Rewrite fractions into equivalent fractions with the common denominator.
 

Step 3: Add and subtract the fractions with common denominators as described above.

Therefore, the LCD is 4.

*Multiply num. and den. by 4.
 

Therefore, the LCD is 15.

*Multiply num. and den. by 5.
 

*Multiply num. and den. by 3.
 

*Div. the common factor of 3 out of both num. and den.

To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that  problem.  At the link you will find the answer as well as any steps that went into finding that answer.

Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.