Combining Mixed Numbers and Order of
Operations
-
Adding Mixed Numbers
In the last section we learned how to add
and subtract two fractions.
If we have two mixed numbers to add, we can just add
the whole number parts and then add the fraction parts.
Example
Add
2
1
3
+ 2
7
5
Solution
We first add the fractional parts:
2
1 2
x 5 1 x 7
+
=
+
the LCM of 7
and 5 is 35
7
5
35
35
17
=
2
x 5 + 1 x 7 = 10 + 7 = 17
35
Now add the whole number parts
3 + 2 = 5
The final answer is
2
1 17
3
+ 2 =
5
7
5 35
Example
Add
3
5
4
+ 5
4 6
We first add the fractional parts:
3
5 3
x 3 5 x 2
+
=
+
4
6
12
12 The LCM of 4
and 6 is 12
19
=
3
x 3 + 5 x 2 = 9 + 10 = 19
12
7
= 1
3
x 3 + 5 x 2 = 9 + 10 = 19
12
The whole number parts are the numbers from the original mixed fractions and
the one from the 1 7/12.
This extra "1" is analogous to the idea of carrying in addition of
whole numbers. We have
4 + 5 + 1 =
10
The final answer is
3
5
7
4
+ 5
= 10
4 6
12
Exercises
Add
-
3
2
5
+ 8
10 15
Hold mouse over the yellow rectangle for the
solution
![13 13/30](../b/simpli2.gif)
-
5
11
3
+ 2
9 12
Hold mouse over the yellow rectangle for the
solution
![6 17/36](../b/simpli2.gif)
-
Subtracting Mixed Numbers
Subtraction of mixed numbers is similar to addition, in that we treat
the whole numbers separately from the fractional part.
Example
Subtract
3
1
8
- 3
5 6
Solution
We first subtract the fractional parts:
3
1 3
x 6 1 x 5
-
=
-
the LCM
of 5 and 6 is 30
5
6
30
30
13
=
3
x 6 - 1 x 5 = 18 - 5 = 13
30
Now subtract the whole number parts
8 + 3 = 5
The final answer is
3
1 13
8
- 3 =
5
5 6
30
Sometimes, we need to borrow a 1 from the whole number in order to
subtract the fractions.
Example
Subtract
3
7
6
- 3
4 8
Solution
If we try to subtract the fractional parts, we soon see that we
cannot do this.
3
7
6 7
-
=
-
4 8
8 8
Since
6
7
<
8 8
we must borrow from the whole number.
3
3
1 x 4 +
3
7
6
= 5 + 1 = 5
+
=
5
4
4
4
4
Now we can subtract the fractional parts:
7
7 7
x 2 7
-
=
- the
LCM of 4 and 8 is 8
4
8
35 8
7
=
7
x 2 - 7 = 14 - 7 = 7
8
Now subtract the whole number parts
5 - 3 = 2
The final answer is
3
7 7
6
- 3 =
2
4
8 8
Exercises
Subtract
-
5
4
9
- 4
9
21
Hold mouse over the yellow rectangle for the
solution
![5 23/63](../b/simpli2.gif)
-
3
3
7
- 3
10
4
Hold mouse over the yellow rectangle for the
solution
![3 11/20](../b/simpli2.gif)
-
Fractions and Order of Operations
The same rules of order of
operations apply to expressions with fractions. In particular, the
order is:
-
Parentheses
-
Exponents
-
Multiplication and Division
-
Addition and Subtraction
With left to right when there is a
tie.
The pneumonic, "Please
Excuse My Dear Aunt Sally" could help us remember this order.
Example
1
4 7
+
x
3 7
30 Multiplication
comes before addition
1
2
24
17
=
+
x
3
15
17
1530
1 x
5
2
7
=
+
=
15
15
15
Example
2
16
=
÷
Exponents
come first
3 25
12
25
25
1
=
x
=
or 1
3 816
24
24
Exercises
Evaluate using the correct order of operations
-
6
1
11
- ÷
7
3 21
Hold mouse over the yellow rectangle for the
solution
![17/77](../b/simpli2.gif)
-
Hold mouse over the yellow rectangle for the
solution
![17/24](../b/simpli2.gif)
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