Ex: These are proper fractions:
FRACTIONS 1 |
Proper and Improper Fractions and Mixed Numbers
Fractions represent division!!
A proper fraction is one in which the numerator is less than ( < ) the denominator.
Ex: These are proper fractions:
An improper fraction is one in which the numerator is greater than ( > ) or equal to ( = ) the denominator.
Ex: These are improper fractions: 
A mixed number consists of an integer (whole number) followed by a proper fraction.
Ex: These are mixed numbers: 
Improper fractions can be turned into mixed numbers by performing the division that the fraction indicates. Fractions represent division, and with an improper fraction, since the numerator is greater than or equal to the denominator, we can divide to find the mixed number equivalent to the fraction.
So, 
and 
We could do the 2nd question simply by saying 11 divided by 3 equals 3 with 2 left over as a remainder. But that 2 had to be divided by 3, so the answer is 3 and 2 thirds –
which means 3 times 1 and 2 times a third.
To turn an improper fraction into a mixed number,
divide the numerator by the denominator then
write the remainder over the denominator.
Sometimes, we have to change a mixed number into an improper fraction. Well, since multiplication is the inverse operation of division, we multiply the integer part of the mixed number, by the denominator of the fraction part and then add the fraction's numerator to the result.
When we do this, we're really multiplying the whole number (integer) part by a fraction equal
to 1, because its numerator equals its denominator – which is the denominator of the fraction part
of the mixed number we began with.
Ex: 
Had the fraction's denominator been 5, we would have multiplied the integer part of the
mixed number by 5 over 5 instead of 7 over 7.
To turn a mixed number into an improper fraction,
multiply the integer part by the denominator then
add the numerator of the fraction part to it,
and put the total over the denominator.
Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.
Practice
1) Decide whether each value is a proper or improper fraction.
Write "proper" beside proper fractions. Change improper fractions into mixed numbers.
a)  |
b)  |
c)  |
d)  |
e)  |
2) Change these mixed numbers into improper fractions.
a)  |
b)  |
c)  |
d)  |
e)  |
.
Solutions
1) Decide whether each value is a proper or improper fraction.
Change improper fractions to mixed numbers.
a)  proper |
b)  |
c)  |
d)  proper |
e)  |
2) Change these mixed numbers to improper fractions.
a)  |
b)  |
c)  |
d)  |
e)  |
