 |
If you'd like a more thorough preparatory tutorial, click here! |
FRACTIONS FAST FACTS
|
If you'd like a more thorough preparatory tutorial, click here! |
///terminology and
definitions///numerator and
denominator///reducing///
///proper and
improper///mixed
numbers///building fractions///
///adding and
subtracting///least common denominator///
///converting mixed numbers to improper
fractions///multiplying and
dividing///
///denominators of
1///zeros within a fraction///
Fractions are parts of a
whole. They are not indicating how
large the whole is. Rather, they describe what part of the whole is
represented.
| col 1 | column 2 | thisis column 3 | Hey! No color for me? | Me, too! |
Three out of five portions are shaded. Therefore this
diagram represents
.
The denominator tells
into how many parts the whole is
divided; the numerator indicates the represented number of pieces of
the whole. For example, in the fraction "three-fourths":
The 3 is the numerator; the 4 is the denominator. There are four parts that make up the whole. Only three of those parts are being referred to.
A fraction can be reduced if the numerator and denominator are evenly divisible by the same number. Divide both the numerator and denominator by the same number. The resulting numerator and denominator create the reduced fraction.
An improper fraction- the numerator is larger than the denominator indicating a whole or mixed number.
A mixed number - a whole number and a proper fraction indicating whole number(s) plus a part of a whole.
Building a fraction to a higher denominator is required when combining fractions with different denominators. To build the fraction to a higher denominator, both numerator and denominator must be multiplied by the same factor. This gives an equivalent fraction which can be reduced to yield the original fraction.
When all of the denominators are the same, numerators can be added or subtracted and placed over the same denominator.
To add and subtract fractions with different denominators, find the lowest common denominator of all of the denominators.
If all numbers are prime (no factors other than "1"), simply multiply them to obtain the lowest common denominator.
Ex. The LCD (lowest common denominator) for the fractions
..... 3 times 5 which equals 15
* * *
If the numbers are composites (have factors other than"1"), find the prime factors of each number.The lowest common denominator contains all of the factors of each number the highest number of times each occurs in any one of the numbers. There are several ways to do this (factor trees, factor boxes, etc.).
Ex. The LCD for the fractions
is the same as
. The LCD must have factors of 2, 3 and 7. The LCD is (2)(3)(7) or 42.
Changing a mixed number into an improper fraction is required when multiplying and dividing. (This is also a practice with addition and subtraction in some later courses.)
To change a mixed number into an improper fraction, multiply the whole number times the denominator and add the numerator of the fraction, place the new number over the original denominator. The numerator will be larger than the denominator indicating that it is really a mixed number disguised as an improper fraction (mixed numbers are good answers, but difficult to work with).
A fraction with zero in the numerator equals 0. A fraction with zero in the denominator is undefined or meaningless.
To divide fractions, write the original first fraction with no changes and invert the second fraction and multiply.
Back to Fast Facts Directory
Back to On Line Math Learning Center Home Page
OK. Quiz me on Fractions!