ADDING AND SUBTRACTING MIXED NUMBERS
Adding:
EXAMPLE EXAMPLE
If the denominators are
the same: ONE: TWO:
3 5
1. Add the numerators.
1 4
5 8
2. Add the whole numbers
1 1
+ 2 +1
5 8
3. Reduce if possible. ----------- ------------
4 6 3
3 5 =5
If the denominators are 5 8 4
different:
EXAMPLE EXAMPLE
1. Create equivalent ONE: TWO:
fractions using LCM.
2 10 1 3
3 = 2 =
2. Add numerators 3 15 4 12
3. Add whole numbers 2 6 1 4
+ 4 = + 3 =
5 15 3 12
4. Reduce if possible
--------------------- ---------------------
16 1 7
7 =1 5
15 15 12
1 1
7+1 =8
15 15
Subtracting:
EXAMPLE ONE: EXAMPLE TWO:
With no renaming
3 2 4
5 6 =
(borrowing), follow addition 4 3 6
as above 1 1 3
- 2 - 4 =
4 2 6
--------------- ----------------------
2 1 1
3 =3 2
4 2 6
Subtracting: With
renaming/borrowing.
EXAMPLE:
If denominators are the
same: 1 5 1 5 6
Method 1:
1. 3 4+ 2. 3 4+ =
5 5 5 5 5
1. Borrow 1 from the whole
number and change what
3 3
-2 - 2
you borrowed into a 5 5
fraction with the same ----------------- ------------------------
denominator.
2. Add what you borrowed 1 5 6
to the fraction you started 3 34 + =
with.
5 5 5
3. Subtract the 3
4. – 2
numerators 5
--------------------
4. Subtract the whole 3
numbers. 1
5
5. Reduce if possible. ______________________________________
1 21
Method 2: 5 =
4 4
1. Change both mixed
numbers to improper 3 11
-2 =
fractions. 4 4
---------------
2. Subtract numerators.
10 2 1
=2 =2
3. Change back to a mixed 4 4 2
number.
Method 1: or Method 2:
4. Reduce if possible.
1 2 4 6 1 13 26
5 6 = + = 6 = =
If denominators are 2 4 4 4 2 2 4
different:
3 3 7 7
1. Create equivalent -1 -1 = =
fractions using LCM. 4 4 4 4
-------------------------- --------------------------
2. Follow steps above. 3 19 3
4 = 4
4 4 4