Contents:
A fraction is a ratio of two integers, or one integer divided by another integer. Note: the fractions below are shown with either with a bar or a slash separating the numerator from the denominator.
- Numerator: is the upper integer on top of the line 2/.
- Denominator: is the lower integer underneath the line /3.
- Proper Fraction: where the upper integer is smaller than the lower integer, ie. 2/3 or
.
- Improper Fraction: where the upper integer is greater than the lower integer, ie 3/2 or
.
- Mixed Number: is where a number is made up of an integer and a proper fraction, ie. 3/2 as a mixed number is: 1
.
- Common Denominator: is necessary when adding or subtracting. The fractions have to be of the same type; have the same value denominator, done by increasing the numerator by the same vale as the increase on the denominator.
Equivalent fractions may be expressed in different ways, but using equivalent ratios, eg. 3/4 is equivalent to 48/64, both upper and lower integers have been increased equivalently. Similarly, 12/16 is equivalent to 3/4, both upper and lower integers have been decreased equivalently to bring the fraction down equivalently to lower terms.
Examples of equivalent fractions:
A fraction at its lowest terms is where the upper and lower integers are decreased equivalently until at their smallest numbers, ie. 2/4 brought down to the lowest terms is 1/2.
Examples of lowest terms:
Operations:
Only fractions of the same type, ie. same denominator, may be added or subtracted. A common denominator is found using equivalent fractions. Then add or subtract the fractions. If necessary convert to a mixed number. Conclude by showing the fraction in its lowest terms.
Example:
Step 1: Find a common denominator: 12. (Both 3 and 4 are factors of 12). The first fraction has the denominator increased by 4 times, therefore the numerator is increased by 4 times (equivalent factors), and the second fraction has the denominator increased by 3 times therefore the numerator is increased by 3 times. The fraction now becomes:
+
Step 2: Now the fractions can be added:
=
.
Step 3:
.
Step 4: The fraction is already at its lowest terms.
Top of Page
Top of Addition & Subtraction
The rules for multiplication and division are different from addition and subtraction. The denominator need not be made the same value. However a mixed number must be converted back to an improper fraction.
For multiplication just multiply the numerators together for the top, and multiply the denominators together for the bottom.
For division invert the fraction that is dividing and use the multiply rule above.
Example 1: Multiplication:
Step 1. Multiply the numerators: 3 x 3 = 9.
Step 2. Multiply the denominators: 2 x 4 = 8.
Step 3. Result: 9/8, if necessary change back to a mixed number: 1
.
Example 2: Division:
Step 1: Invert the dividing fraction:
.
Step 2: Multiply the numerators: 3 x 4 = 12.
Step 3: Multiply the denominators: 3 x 2 = 6.
Step 4: Result: 12/6, if necessary change back to a mixed number: 2.
Examples of the four operations:
(Note: there is no attempt to reduce to lowest terms or improper fractions.)
Top of Page
©Mathstutor.com 2001-2005
