Operations with rational numbers

2. Any number that can be made by dividing
one integer by another. The word comes from
"ratio".
This means that rational numbers include
positive and negative numbers, whole
numbers, fractions and decimals.
a
b

3. Two fractions that stand for the same number

4. Mixed
Numbers
Improper
Fractions

5. The sum of a whole
number and a fraction

6. &
These are examples of
mixed numbers

7. A fraction with a numerator greater then
the denominator

NUMERATOR
denominator

8. These are examples
of improper
fractions
&

9. =
=

10. =

11. = =

12. = =

14. Adding
Fractions
Subtracting
Fractions
Multiplying
Fractions
Dividing
Fractions

15. Adding fractions requires a common
denominator
To find the common denominator
between fractions simply multiply the
denominators and this is the common
denominator.
this number may be large so try and find a
number that all denominators will divide into
evenly.

16. However this number may be large so
try and find a number that all
denominators will divide into evenly.
Adding fractions requires a common
denominator
To find the common denominator
between fractions simply multiply the
denominators and this is the common
denominator.

17. We need to find a C.D. in order to add these
fractions.
If we multiply the denominators
that is a big number…but both 6 and 12 divide
evenly (without a remainder) into 12.
The first fraction already has a denominator of 12
so we leave it alone but what do we have to
multiple the second denominator by in order to
change it to 12?
If you said 2…you are right!
2 4
12 6
+
12 6 72´ =

18. If you multiply the
denominator by 2
you MUST multiply
the numerator by
two also!
Remember:
whatever you do to
the bottom you
must do to the top.
Once you have
common
denominators…add
the numerator and
KEEP the Common
Denominator.
2 4
12 6
2 4 2
12 6 2
2 8
12 12
10
12
+
´
+
´
+

20. Same rule…you have to get a
common denominator before you
subtract the numerators!

21. 3 2
4 5
3 5 2 4
4 5 5 4
15 8
20 20
15 8
20
7
20
-
´ ´
-
´ ´
-
-

23. Multiplying fractions is easy
Multiple the numerators
Multiple the denominators

24. 1 2
3 5
1 2
3 5
2
15
´
´
´

26. Dividing fractions requires one more
step
Keep the first fraction the same
Change the multiple to divide
And FLIP the second fraction

27. 2 6
5 7
2 7
5 6
2 7
5 6
14
30
¸
´
´
´
When the fraction
is “flipped” it is
called the
INVERSE