Transcript Lesson 5-4a

5-4
6th grade math
Adding and Subtracting with Unlike
Denominators
Objectives
• To add and subtract fractions and mixed
numbers with unlike denominators
California State Standards
• NS 2.4
: Determine the LCM of whole
numbers; use them to solve problems with
fractions (e.g., to find a common denominator to
add two fractions and to find the reduced form
for a fraction)
• NS 2.0
: Calculate and solve problems
involving addition, subtraction, …
• NS 2.1: Solve problems involving addition,
subtraction, … of positive fractions and explain
why a particular operation was used for a given
situation
Vocabulary
• Unlike denominators
– Fractions with denominators that are not the same
• ,
• Like denominators
– Fractions with denominators that are the same
• ,
• Least Common Denominator (LCD)
– the LCM of the denominators of two or more fractions
• 12 = LCD of ¼ and 
• Equivalent Fractions
– Fractions that name the same number
•  = 2/4 = 4/8 = 5/10 , …
How to solve subtracting with unlike
1) LCD = 12
denominators
 -
1. Find the LCD of the
fractions
2. Write the equivalent
fractions
3. Subtract.
4. Simplify, if possible
2) 3 = x 3 = 9
4 = x 3 = 12
1=x4= 4
3 = x 4 = 12
3) 9 - 4 =
12 12
5
12
How to add with unlike denominators
5 + 2
12 15
1. Find the LCD of the
fractions
2. Write the equivalent
fractions
3. Subtract.
4. Simplify, if possible
1) LCD = 60
2) 5 x 5 = 25
12 x 5 = 60
2x4= 8
15 x 4 = 60
3) 25 + 8
60 60
=33
60
4) Divide by 3 = 11
Divide by 3 = 20
How to add w/unlike denominators and
“mixed/impropers”
8  + 10  =
8  + 10 
1. Write equivalent
fractions.
2. Add.
3. Simplify, if possible .
1. LCD = 12
2x4=8
3x3= 9
3 x 4 = 12 4 x 3 = 12
2) 8 8 + 10 9 =
12
12
3) = 18 17 = 18 + 1 5 = 19 5
12
12
12
How to subtract w/unlike
denominators and “to borrow”
6 -4
1) Write the equivalent
fractions using the LCD.
2) Rename.
3) Subtract.
4) Simplify, if possible.
6 -4
1) LCD = 8
1x4=4
2x4=8
=63 - 44
8
8
2) = 5 8+3 - 4 4
8
8
3) = 5 11 - 4 4
8
8
4) = 1 7
8
Try It!
1) 8/9 + 4/ 15
1) 1 7/45
2) 1/9 + 1/6 + 1 /30
2) 14/45
3) ½ - 1/10
3) 2/5
4) 7/8 – 9/32
4) 19/32
How it works …
1) 8/9 + 4/ 15
LCD = 45
8 x 5= 40 + 4 x 3 = 12
9 x 5 45 15 x 3 = 45
40 + 12 =
45
45
52 = 1 7
45
45
2) 1/9 + 1/6 + 1 /30
LCD = 90
1 x 20 = 20 1 x 30 = 30 1x 6 =
6
9 x 20 = 180 6 x 30 = 180 30 x 6 = 180
20 + 30 + 6 = 56
180
180
Divide by 4 = 14/45
3) ½ - 1/10
LCD = 10
½ = 5/10
= 5 -1
10
= 4/10 = 2/5
4) 7/8 – 9/32
LCD = 32
7 x 4 = 28
8 x 4 = 32
= 28 – 9
32
= 19
32
Try Some More!
5) 9 ¼
+2
11 7
12
7) 12
- 3 7/10
8 27
40
6) 6 13/15
+ 4 2/33
10 51
55
8) 6
- 4
1 10
21
How it works…
5) 9 ¼ = 9 3/12
+ 2  = + 2 4/12
11 7
12
6) 6 13/15 = 6 143/165
+ 4 2/33 = + 4 10/165
10 153 =
165
10 51
55
7) 12 = 12 15/40
- 3 7/10 = 3 28/40
8 27
40
8) 6 = 6 3/21
- 4  = - 4 14/21
5
21 + 3/21 = 5 24/21
- 4 14/21
1 10
21
Objectives Reviewed
Why?
• To add and subtract
fractions and mixed
numbers with unlike
denominators
You are learning all number
sense skills: add and
subtract whole numbers,
decimals, and
fractions/mixed fractions.
Independent Practice
• Complete problems
12-23.
• For an extra challenge,
try 24-27.
• Remember to show all
work.
• Copy the original
problem before
solving.
• If time, complete the
Mixed Review
problems: 28-37.
• If still more time,
complete Accelerated
Math.