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EAP, 1/2011 LSC-O
Definition: A fraction is a numerical representation for
part of a whole.
Add all the pieces to get
the whole:
Fact:
The fraction bar represents division ( ÷ ), so Any fraction with a Denominator of 1 is equal to its Numerator: Division by zero is Undefined, so the Denominator of a fraction can never be zero:
Fundamental Property of Fractions...
*We use this fact when we Reduce (or Simplify ) fractions to lowest terms.
Equality of Fractions...
if and only if *We use this fact when we Cross Multiply to solve for an unknown numerator or denominator.
Addition and Subtraction of fractions
require a common denominator.
When the denominators are different, multiply one or both fractions by another fraction that is the equivalent of 1 to create a Common Denominator ; then add or subtract. You may be able to multiply the smaller Denominator by something to create the larger one: If not, then multiply the two Denominators together:
Multiplication and Division of fractions do
not require a common denominator.
Note that it is easier to reduce before actually multiplying. To divide fractions, first invert the Divisor (second fraction) to get its Reciprocal ; then multiply. Factoring before multiplying can help with reducing: 1/
The DENOMINATOR tells how many equal pieces the whole is divided into. The NUMERATOR tells how many pieces of the whole the fraction represents. Page 1 of 2
EAP, 1/2011 LSC-O A Proper Fraction has a numerator that is smaller than its denominator and represents a quantity less than the whole, or < 1 : 1/5 , 2/5 , 3/5 , and 4/5 are proper fractions. An Improper Fraction has a numerator larger than its denominator and represents a quantity greater than the whole, or > 1: 6/5 , 10/5 , and 27/5 are improper. Mixed numbers , such as are whole numbers and portions less than 1 (fractions) added together. It is often useful in doing calculations to convert mixed numbers to improper fractions. To do so, change the whole number to a fraction with the same denominator as the other fraction and add:
A quick way: (WHOLE NUMBER X DENOMINATOR + NUMERATOR)/DENOMINATOR:
To go from improper fraction to mixed number , simply divide the Numerator by the Denominator. The Remainder over the Divisor is the fractional portion. Comparing fractions... Obviously 5/8 > 3/8 , but what about 5/8 and 7/12? Here’s how to tell: Express each fraction with a Common Denominator : Or, express each as a decimal: Also, test for Equality of Fractions : Eliminating fractions... A fraction multiplied by its Reciprocal equals 1 ; use this fact to isolate x and solve an equation: Multiply through by the Least Common Multiple (LCM) of the denominators replaces fractions with whole numbers, making an equation easier to work with:
From Decimals to Fractions to Percents...
Decimals can be expressed as fractions with a Denominator that is a Power of 10. The number of digits behind the decimal tells how many zeros belong in the denominator. Remember to reduce fractions when possible: To express a fraction as a percent, first divide the Numerator by the Denominator ; then multiply the resulting decimal number by 100 (or, simply move the decimal two places to the right): 1 / 2 = .50 = 50%, 1 / 4 = .25 = 25%, 9 / 40 = .225 = 22.5%, and 1 / 1 = 1.00 = 100%
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