Fraction
A way to express numbers that fall in between integers (though integers can also be expressed in fractional form). A fraction expresses a part-to-whole relationship in terms of a numerator (the part) and a denominator (the whole).
Example:
(7/2) is equivalent to the decimal 3.5.
Numerator
The top of a fraction. In the fraction, (7/2), 7 is the numerator.
Denominator
The bottom of a fraction. In the fraction (7/2), 2 is the denominator.
Proper Fraction
Fractions that have a value between 0 and 1. The numerator is always smaller than the denominator. (1/2) is a proper fraction. (3/2) is not a proper fraction.
Improper Fraction
Fractions that are greater than 1; can also be written as a mixed number. (7/2) is an improper fraction. This can also be written as a mixed number: 3 (1/2).
Mixed number
An integer combined with a proper fraction; can also be written as an improper fraction. 3 (1/2) is a mixed number. This can also be written as an improper fraction: (7/2)
Complex fraction
A fraction in which there is a sum or difference in the numerator or denominator.
Example:
(3+6)/10 is one example.
10/(3+6) is another.
Simplifying Fractions
Reducing numerators and denominators to the smallest form. Dividing the numerator and denominator by the same number does not change the value of the fraction.
Example:
Given (21/6), we can simplify by dividing both the numerator and the denominator by 3. The simplified fraction is (7/2).
Reciprocal
The product of a number and its reciprocal is always 1. To get the reciprocal of an integer, put that integer on the denominator of a fraction with numerator 1. The reciprocal of 3 is (1/3).
Note:
To get the reciprocal of a fraction, switch the numerator and the denominator. The reciprocal of (2/3) is (3/2).
Dividing Fractions
Change the divisor into its reciprocal and then multiply.
Example:
Given (3/5) / 2, take the reciprocal of 2. The reciprocal is (1/2). Now multiply: (3/5) * (1/2) = (3/10).
Common Denominator
When adding or subtracting fractions, we first must find a common denominator, generally the smallest common multiple of both numbers.
Example:
Given (3/5) + (1/2), the two denominators are 5 and 2. The smallest multiple that works for both numbers is 10. The common denominator, therefore, is 10.
Adding or subtracting fractions
Adding or subtracting fractions: always simplify within a given numerator and denominator, but do NOT simplify across fractions. Instead, find a common denominator first and only then combine the two (or more) numerators.
Example:
Given (3/5) + (2/4), we can simplify (2/4) to (1/2). The simplified problem is (3/5) + (1/2). The common denominator is 10. Multiply the first fraction by 2 and the second fraction by 5 to get (6/10) + (5/10). Next, add the numerators and keep the same denominator to get (11/10).
