9.7 Add and Subtract Negative Mixed
Numbers with Different
Denominators
Common Core Standards
7.NS.1. Apply and extend previous understandings of addition and subtraction
to add and subtract rational numbers; represent addition and subtraction on a
horizontal or vertical number line diagram. a. Describe situations in which
opposite quantities combine to make 0. For example, a hydrogen atom has 0
charge because its two constituents are oppositely charged.
7.EE.3. Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers, fractions,
and decimals), using tools strategically. Apply properties of operations to
calculate with numbers in any form; convert between forms as appropriate; and
assess the reasonableness of answers using mental computation and
estimation strategies. For example: If a woman making $25 an hour gets a 10%
raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new
salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center
of a door that is 27 1/2 inches wide, you will need to place the bar about 9
inches from each edge; this estimate can be used as a check on the exact
computation.
WARM-UP
Evaluate the expressions.
1 3
1)
+
2 4
1 ⎛ 3⎞
2) − + ⎜ − ⎟
2 ⎝ 4⎠
1
3
3) 5 + 2
2
4
1 ⎛ 3⎞
4) −5 + ⎜ −2 ⎟
2 ⎝ 4⎠
5) What mixed number problems are represented below?
-3
1
a) − 1 + 2
4
-2
-1
1
1⎞
⎛
b) − 1 − ⎜ −2 ⎟
⎝ 4⎠
2
3
1
c) − 1 − 2
4
Add and Subtract Negative Mixed
Numbers with Different Denominators
How do we add negative mixed numbers with
different denominators?
1 ⎛ 3⎞ ⎛
5 ⎞
− + ⎜ −1 ⎟ + ⎜ −1 ⎟
2 ⎝ 8 ⎠ ⎝ 16 ⎠
8 ⎛
6 ⎞ ⎛
5 ⎞
−
+ ⎜ −1 ⎟ + ⎜ −1 ⎟
16 ⎝ 16 ⎠ ⎝ 16 ⎠
19
3
−2
= −3
16
16
NOTES
For negative mixed numbers, we still want to find the
LCD first.
Examples
Evaluate the expressions.
3 ⎛
1⎞
−2
+ ⎜ −6 ⎟
10 ⎝ 5 ⎠
1
3
−4 + 6
2
4
EXAMPLES
Evaluate the expressions.
3 ⎛ 1⎞
−2 + ⎜ − ⎟
5 ⎝ 4⎠
EXAMPLES
Evaluate the expressions.
1 ⎛
1⎞
1 − ⎜ −3 ⎟
3 ⎝
4⎠
7 ⎛ 3⎞
−5 − ⎜ −2 ⎟
8 ⎝ 4⎠
NOTES
If the whole number and fraction part have different
signs we need to regroup.
Examples
Evaluate the expressions.
1 ⎛
5 ⎞
3 + ⎜ −2 ⎟
5 ⎝ 10 ⎠
7 ⎛
1⎞
−1 − ⎜ −4 ⎟
8 ⎝ 2⎠
EXAMPLES
Which mixed number problems are represented
below?
-3
1
1
a) − 2 + 2
4
2
-2
-1
0
1
1 ⎛
1⎞
b) − 2 − ⎜ −2 ⎟
4 ⎝ 2⎠
2
3
1
1
c) − 2 − 2
4
2
EXAMPLES
Which mixed number problems are represented
below?
-3
1
1
a)1 − 2
2
4
-2
-1
0
1
1 ⎛
1⎞
b)1 + ⎜ −2 ⎟
2 ⎝ 4⎠
2
3
1 ⎛
1⎞
c)1 − ⎜ −2 ⎟
4 ⎝ 4⎠
EXAMPLES
Which is closest to the exact answer?
3 ⎛
1⎞
−5
+ ⎜ −4 ⎟
16 ⎝ 8 ⎠
a) − 9
b)1
c)9
c) − 11
PRACTICE
Evaluate the expressions.
3
5
−6 + 2
7
14
1
3
3 −2
6
4
2 1
−7 −
5 3
FINAL QUESTION
Which mixed number problems are represented
below?
-3
1 1
a) − 2 −
4 2
-2
-1
0
1
1 ⎛ 1⎞
b) − 2 − ⎜ − ⎟
4 ⎝ 2⎠
2
3
1 ⎛ 1⎞
c) − 2 + ⎜ − ⎟
4 ⎝ 2⎠