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!