Fractions

Page 1

The fraction

is called a proper fraction. The fractions

and are improper fractions.

Definition:

A proper fraction is a fraction in which the

numerator is less than the denominator.

Definition:

An improper fraction is a fraction in which the

numerator is greater than or equal to the denominator.

In example 1, we will identify each fraction as proper or improper. We will

also write each fraction using words.

Example 1

Fraction

Type

Words

improper

three-halves

proper

two-fifths

improper

three-thirds

proper

five-sixths

improper

eleven-eighths

improper

eight-eighths

What do the fractions in example 2 have in common?

Example 2

two-halves

three-thirds

four-fourths

five-fifths

six-sixths

In example 2, each fraction has a numerator that is equal to its denominator. Each of these fractions

is an improper fraction, equal to one whole (1). An improper fraction can also be greater than one

whole, as shown in example 3.

Example 3

In the improper fraction seven-fourths, the numerator (7) is greater than the denominator (4). We can

write this improper fraction as a mixed number.

Definition:

A mixed number consists of a whole-number part and a

fractional part.

Page 2

1. Fraction addition - common denominators

Add the numerators, and use the common denominator2. Fraction addition - different denominators

First find a common denominator by taking the least common multiple

of the denominators. Then convert all the addends to have this common

denominator. Then add using the rule number 1. 3. Finding equivalent fractions

Multiply both the numerator and denominator by a same number.4. Convert a mixed number to a fraction

Multiply the whole number part by the denominator and add the

numerator to get the numerator. Use the common denominator as in the

fractional part of the mixed number.5. Convert an improper fraction to a mixed number

Divide the numerator by the denominator to get the whole number

part. The remainder will be the numerator of the fractional part.

Denominator is the same.6. Simplifying fractions

Find the (greatest) common divisor of the numerator and denominator, and divide both by it.7. Fraction multiplication

Multiply the numerators and the denominators.8. Fraction division

Find the reciprocal of the divisor, and multiply by it.9. Comparing fractions

Convert the fractions so they have a common denominator. Then compare the numerators.10. Convert fractions to decimals

Example, divide 5 by 8 and the answer would be a decimal