1. A fraction denotes some part of a whole. It also
denotes a quotient of two whole
numbers.
2. A fraction is any number that can be written in the form
where a and b are
whole numbers and b is not zero .
3. The parts of a fraction are: 
The line
that separates the
numerator and the denominator is called the fraction line.
4. Divide a whole into an equal number of parts. That number goes in the
denominator (bottom) of the fraction.
How many of these parts are you considering? This number goes in the
numerator (top) of the fraction.
5. Suppose n is any number except 0. Recall:
undefined
6. A proper fraction is a fraction whose numerator
is smaller than its denominator.
It is less than 1.
An improper fraction is a fraction whose numerator is greater than or
equal to its
denominator. It is greater than or equal to 1.
7. A mixed number is a whole number and a proper fraction. (For example:
1 ½
which means 1 + ½ .)
An improper fraction can be written as a mixed number and visa versa.
8. Write mixed numbers as improper fractions: (See page 77.)
Step 1: Multiply the whole number by the denominator.
Step 2: Add this product from step 1 to the numerator of the fraction.
Step 3: Write the sum found in step 2 over the original denominator.
9. Write an Improper Fractions as a Mixed Number or a
Whole Number: (See
page 78.)
Step 1: Divide the denominator into the numerator.
Step 2: The quotient becomes the whole number. The fraction part is the
remainder over the original denominator. (If the remainder is zero, the
fraction re presents a whole number – the quotient.)
10. Fractions that represent the same portion of the whole are equivalent
fractions .
11. To write a fraction as an equivalent fraction with a different
denominator (a
multiple of the original denominator), multiply the numerator and the
denominator of the original fraction by the number needed to obtain the desired
denominator.
If a, b, and n are whole numbers with b ≠ 0 (b not 0),
(This is just multiplying the original fraction by 1 so
the value has not changed ;
just the form of the fraction has changed.)
12. A property of equivalent fractions is that their cross products are equal.
That is:
if 
, then ad = bc.
This property can be used to check to see if two fractions are equivalent.
13. A fraction is written in simplest form or lowest terms if the
numerator and
denominator have no common factors other than 1.
14. The process of writing a fraction in simplest form is called simplifying
the
fraction.
15. To simplify a fraction, factor the numerator and denominator (possibly using
their prime factorizations) and cancel (or divide out) common factors.
This is true because:
16. Caution: Recall that 1 is always a factor of
any number. Thus, if you cancel all
of the factors in a numerator or denominator, there is still a 1 left. (But a
one in
the denominator simplifies as just the whole number given in the numerator.)
17. Like fractions have the same denominators. Unlike fractions have
different
denominators.
18. Compare fractions to see which of two or more fractions is larger:
Write the fractions as equivalent fractions with the same denominators.
This denominator must be a multiple of all of the denominators. So the
best denominator to use is the LCM of all of the denominators . The LCM
of denominators is also called the least common denominator ( LCD ).
The one with the largest numerator is then the larger of the fractions.
