1
15
2
5
REDUCING FRACTIONS
1.
2.
3.
Find the largest number that will go into the top and
bottom
Divide that number into top and bottom to make a new
fraction
Repeat steps if necessary
2 divides
evenly
Examples:
2
8
12
=
15
6
9
= 1
4
10
=
20
4
5
= 2
3
1
2
CHANGING FORMS of FRACTIONS
Improper to Mixed
Look at the
fraction like a
division problem
2
17 =
5 3
3
3
11
=2
4
4
“Four goes into eleven 2 whole
times with 3 left over out of 4”
Mixed to Improper
Examples:
2
34 =
4 8
8
(reduced)
4
1
4
+3
2 x4 =
11
4
Examples:
Start with the bottom number
1.
Multiply the bottom by the whole
number.
2. Add the top to that amount.
3. Put that number as the new top
number
4. Keep the bottom number the same.
6
13
1
=
2
2
3
26
5
=
7
7
GETTING COMMON DENOMINATORS
See if the largest bottom number is a
number the other bottoms will divide
into evenly. If it does, use it as your
common denominator
If not, find the lowest number
that both denominators will
divide into evenly.
Examples:
x3
2
6
= 15
5
1 x5 5
=
3
15
ADDING FRACTIONS
1. Get Common
Denominators
2. Change top numbers
where necessary
3. Add the top
numbers
4. Keep the same
bottom number
5. Add whole numbers
if there are any
6. Reduce or change
form if needed
+
2
3
1
6
x2
=
=
4
6
1
6
5
6
x5
1
5
=
3
15
2 x3 6
1 5 = 15
3
+
4 11
15
x4
1
4
= 12
3
3 x3 9
=
4
12
x1
7
7
=
16
16
1 x4 4
=
4
16
Change the top numbers if you have
changed the bottom numbers.
Multiply the top numbers by the same
amount as each bottom number.
x2
5
10
=
6
12
3 x3 9
=
4
12
Now, try these practice problems and see if your
answers match up.
1
3
3
1 5
7
+
14
8 15
3
+1
1
3
2
5
11
4 15
2
+1
2
5
3
4
3
4 20
SUBTRACTING FRACTIONS
x2
1.
2.
3.
4.
5.
6.
7.
5
10
= 12
6
1 x3 3
2 4 = 12
7
6 12
8
Get Common
Denominators
Change top numbers
where necessary
Subtract the top
numbers
Borrow if necessary
Keep the same
bottom number
Add whole numbers
if there are any
Reduce or change
form if needed
-
Now, try these practice problems and see
if your answers match up.
3
19 3 1 3
+
20
-
3
8 2
3
9
-
3 61
4
19
This is
3
what we
have now
2
- 8 3
11 23
3
1
2
1
3 3
6
5
6
1
2
2
3
3
3 4
5
-
11
1 12
9 31
MULTIPLYING FRACTIONS
1.
2.
3.
4.
5.
6.
Make sure both numbers
are in fractional form (if
whole numbers—put over 1,
if mixed numbers—change
to improper)
Cancel if you can (reduce
diagonally)
Multiply the top numbers
Multiply the bottom
numbers
Reduce if possible
Change improper fractions
to mixed numbers if
needed.
DIVIDING FRACTIONS
1.
2.
3.
4.
5.
6.
7.
Make sure both numbers
are in fractional form (if
whole numbers—put over 1,
if mixed numbers—change
to improper)
Flip the second fraction and
change to multiplication
Cancel if you can (reduce
diagonally)
Multiply the top numbers
Multiply the bottom
numbers
Reduce if possible
Change improper fractions
to mixed numbers if
needed.
Now, try these practice problems
and see if your answers match up.
2
x 3
3
4
1
2 x
3
5
3
=
4 2
1
x
2
3
6
=
2
3
x
4
6
3
1
x
9
2
10
21
= 16
2
1
x 2 = 11
1
1
11
12
5
x 4
6
7
1
2
=
=
11
1
4
1
2
= 7
Just like multiplying but with one new step (Step 2)
Now, try these practice problems
and see if your answers match up.
1 ¸ 1
2
4
1
1 x
2
2
8
3
42
1
=
2
1
2
=
1 ¸ 5
3
6
6
2 ¸ 1
3
3
¸ 1
3
8
3
1
4
1
x 3 = 8 = 8
1
1
=
1 ¸ 1
2
4
9 ¸
10
1
2
5
= 26
1
6
= 4
1
5