Transcript Fractions

Fractions
Fractions
Numbers such as ½ and -¾ are called
fractions.
 The number above the fraction line is
called the numerator.
 The number below the fraction line is
called the denominator.

Reducing Fractions

When both the numerator and
denominator have a common divisor, we
can reduce the fraction to its lowest
terms.

A fraction is said to be in its lowest terms
(or reduced) when the numerator and
denominator are relatively prime (have no
common divisors other than 1).
To reduce a fraction to its lowest terms,
divide both the numerator and the
denominator by the GCD.
 The fraction 6/10 is reduced to its lowest
terms as follows.

6
62 3


10 10  2 5
You Try…
54
 Reduce to its lowest terms 90
Mixed Numbers and Improper
Fractions
The number 2¾ is an example of a mixed
number. It is called a mixed number
because it is made up of an integer and a
fraction.
 2¾ means 2 + ¾
 An improper fraction is a fraction whose
numerator is greater than its denominator.

The figure shows improper
fractions and mixed numbers….
How do you convert mixed
numbers to improper fractions?
Example: Convert to Improper
Fractions.
How do you convert improper
fractions to mixed numbers?
Example:
number.
1
58
5
____
3
8
Convert
5
to a mixed
3
1
5
Example:
number.
225
Convert
8
to a mixed
Multiplication of Fractions

Multiply the numerators and multiply the
denominators together then reduce if
necessary.
Examples
3 7 3  7 21
 

5 8 5  8 40
  2   4   2  4  8




39 27
 3  9 
7
 7  1   15  9  135
or 4
1  2      
32
 8  4   8  4  32
Reciprocal


The reciprocal of any number is 1 divided by
that number.
The product of a number and its reciprocal
must equal 1.
Division of Fractions

To find the quotient of two fractions,
multiply the first fraction by the reciprocal
of the second fraction.
5 3
 .
7 4
Example: Evaluate
5 4 20
 
7 3 21
Addition and Subtraction of
Fractions

Before we can add or subtract fractions,
the fractions must have a lowest
common denominator.
Adding or Subtracting Fractions
with Unlike Denominators
Use prime factorization to find the LCD for
the denominator.
 Example:

5
3  5 5   3 6  25 18
7

      


12 10  12 5   10 6  60 60 60
Addition Example
Now
Reduce!