Download FRACTIONS, GCF,REDUCING

FRACTIONS AND EQUIVALENT FRACTIONS
Fractions - a part or piece of a whole , or part of a set
This is a proper fraction.
2 numerator
(part)
3 denominator (whole)
Note: when the numerator and denominator are the same, the
fraction is equal to 1 whole.
http://www.visualfractions.com/
Equivalent: equal in value
Examples: 3 + 3 is equivalent to 2 3 (equivalent numerical expressions)
2.9 is equivalent to 2.90
(equivalent decimals)
1 yard is equivalent to 3 feet (equivalent lengths)
is equivalent to
(equivalent fractions)
Equivalent Fractions Two or more fractions that have the same quotient or
that name the same region, part of a set, or part of a segment.
Example:
Remember the “Golden Rule”:
Multiply the numerator and the denominator by the same number to make an
equivalent fraction.
Divide the numerator and denominator by the same number to make an
equivalent fraction.
Notice the pattern with fractions equivalent to 1.
2
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
2 4 6 8 10 12 14 16 18 20 22 24
REDUCING FRACTIONS
Factor –
factor (noun) A number that is multiplied by another to yield a product
Note:a factor of 32 is 8 because 8 4 = 32 , another factor is 4.
Example: the factors of 24 are (1, 2, 3, 4, 6, 8, 12, 24)
Greatest Common Factor (GCF)
The greatest number that is a factor of two or more numbers
Example: the greatest common factor of 12 and 18 is 6.
12 (1,2,3,4,6,12)
18 (1,2,3,6,9,18)
The GCF is 6
Lowest Terms
The form of a fraction in which the numerator and denominator have
no common factor except 1.
Reducing Fraction to Lowest Terms
Divide the numerator and denominator by the GCF.
Example:
1) Find the GCF of the numbers.
2) Divide the numerator and the denominator by the GCF.
Example: 6 (1, 2, 3, 6, )
8 (1, 2, 4, 8, )
More examples:
16 = 4
20
5
4
8
The GCF is 2.
= 1
2
12
18
6 = 3
8
4
= 2
3
Note:
If you don’t divide by the GCF, it may take a few steps to get to
lowest terms.
Example:
If you divide by 2, it is not the GCF, so you must divide again by 3.
12 = 6 = 2
18
9
3
SHORTCUTS TO REDUCE FRACTIONS
1. If the numerator divides into the denominator evenly
(it is the GCF), divide the numerator (GCF) and the denominator
by the numerator. The reduced fraction will have a numerator
of 1 and a denominator equal to the quotient.
5 = 1
35 7
2. If both numbers are even, keep dividing both by 2, but you
must keep dividing until the numerator and denominator have
no common factors except 1.
Ex.
24 = 12 , 12 = 4
30
15 15
5
WAYS TO RECOGNIZE LOWEST TERMS!
1. The numerator of the fraction is 1.
2. The numerator and denominator are consecutive(1 apart)!
3. The numerator and denominator are prime numbers.
4. The numerator is a prime number and it does not divide into
the denominator evenly.