Transcript Adding and Subtracting Unlike Fractions

Warm Up
Add or subtract.
1. 13 + – 2
5
5
2.
3
11
12
–2
7
12
1
1
5
1
1
3
3. 6.5 + (–1.2)
5.3
4. 3.4 – 0.9
2.5
Adding and Subtracting
with Unlike Denominators
Section 2.6
Objectives:
• Add and subtract fractions by using
factoring to find common denominators.
(NS 2.2)
• Add and subtract rational numbers (NS 1.2)
Words to know:
• Least common
• denominator:
least common multiple of the
denominators of two or more fractions.
To add and subtract fractions with
unlike denominators, first find a
common denominator using one of
these methods:
Method 1 Find a common denominator by
multiplying the denominators.
Method 2 Find the least common denominator
(LCD).
Adding Fractions
Use 6 x 9 as the
common denominator.
–
using common denominator
5  2  59   26 

   

6  9  69  96 
Add numerators
45  (12)

54
Simplify
33 11

54 18
33
54
Let’s review… • Do you remember how to find
Least Common Multiple?
12 – 12, 24, 36, 48, 60, 72, 84,
96, 108
20 – 20, 40, 60, 80, 100, 120
How do you find the Least
Common Multiple?
Adding Fractions
The LCM of 6 and
9 is 18.
Add numerators.
Simplify fraction.
– using LCM
5  2  53   2 2 
   


6  9  63  92 
15  (4)

18
11

18
Evaluating
Algebraic
Expressions
The LCM of 2, 4, and 8 is 8.
Simplify
Add numerators
Evaluate the expression x – y + z when
1 3 3
x yz   
2 8 4
1 4 3 3  2
 
24 8 42
4  3 6

 
8  8  8
7
8
x
1
3
3
,y  ,z 
2
8
4
One more
option….
The LCM is 24!
What number can you
multiply each denominator
by to get to 24?
Multiply that number on the
top too!
5
6
3
8
= ●4
=
20
●4
24
●3
●3
9
24
29
5
1
24
24
Try on your own….
7 3
 
12 4
1
6
7 2
11
  1
10 3
30
x
x x
 
4 5
20
2 3
 
a 2
4  3a
2a
Application
Fred and Jose are building a tree house.
3
They need to cut a 6 4 foot piece of wood
and a 4 5 foot piece of wood from a 12
12
foot board. How much of the board will be
left?
12 – 6
3
4
–4 5
12
=
12
1
– 27 –
4
=
144
12
–
=
10
12 ,
or
81
12
53
12
–
53
12
5
6
There will be
5
6
foot left.
How do you add or subtract
fractions with unlike
denominator
Lesson Quiz
Add or subtract.
1. 5 + 1
14 7
2. 8 2 – 11
2
3
1
2
1
76
3. 3 + –2 2
5
3
–2
1
15
9
13
3
4. Evaluate1 – n for n = 16 .
16
8
3
Robert is 5 feet 6 1 inches tall. Judy is 5 feet 3 4
2
inches tall. How much taller is Robert than Judy?
2
3
4 in.