fractions. numbers such as ½ and -¾ are called fractions. the number above the fraction line is...
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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.
5
3
210
26
10
6
You Try…
Reduce to its lowest terms 90
54
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: Convert to a mixed number.
5
8
3
____
5
185
5
31
Example: Convert to a mixed number.
8
225
Multiplication of Fractions
Multiply the numerators and multiply the denominators together then reduce if necessary.
Examples
32
74
32
135
4
9
8
15
4
12
8
71
27
8
93
42
9
4
3
2
40
21
85
73
8
7
5
3
or
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.
Example: Evaluate .4
3
7
5
21
20
3
4
7
5
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:
60
7
60
18
60
25
6
6
10
3
5
5
12
5
10
3
12
5
Addition Example
NowReduce!