Transcript Slide 1

Adding and Subtracting
5-2 with Unlike Denominators
Learn to add and subtract fractions with
unlike denominators.
Adding and Subtracting
5-2 with Unlike Denominators
Vocabulary
least common denominator (LCD)
Adding and Subtracting
5-2 with Unlike Denominators
1
The Pacific Ocean covers __ of Earth’s surface. The Atlantic
3
1
Ocean covers __ of Earth’s surface. To find the fraction of
5
Earth’s surface that is covered by both oceans, you can add
1
__
and 5 , which are unlike fractions.
1
__
3
Adding and Subtracting
5-2 with Unlike Denominators
To add or subtract unlike fractions, first
rewrite them as equivalent fractions with a
common denominator.
Remember!
Fractions that represent the same value are
equivalent.
Adding and Subtracting
5-2 with Unlike Denominators
Additional Example 1: Cooking Application
Mark made a pizza with pepperoni covering
1
__
of the
4
1
__
pizza and onions covering another
. What fraction of
3
the pizza is covered by pepperoni and onions?
1
1
Add __
+ __
.
4
3
1
__
4
1
__
+
3
_____
1
__
4
1
__
3
?
Find a common denominator for 4 and 3:
4 x 3 = 12.
Adding and Subtracting
5-2 with Unlike Denominators
Additional Example 1 Continued
1
__
4
3
__
12
1
4
__
__
+
3 _____
12
_______
7
__
12
Write equivalent fractions with 12 as the
common denominator.
Add the numerators. Keep the common
denominator.
1
__
4
1
12
1
12
1
__
3
1
12
The pepperoni and onions cover
1
12
1
12
1
12
1
12
7
__
of the pizza.
12
Adding and Subtracting
5-2 with Unlike Denominators
Check It Out: Example 1
1
Tori made a pizza with peppers covering __
of the pizza
3
1
__
and ham covering another
. What fraction of the pizza
2
is covered by ham and peppers?
1
1
Add __ + __ .
3
2
1
__
3
1
__
+
2
_____
1
__
3
1
__
2
?
Find a common denominator for 3 and 2:
3 X 2 = 6.
Adding and Subtracting
5-2 with Unlike Denominators
Check It Out: Example 1 Continued
2
__
6
Write equivalent fractions with 6 as the
common denominator.
1
3
__
__
+
2 _____
6
_______
Add the numerators. Keep the common
denominator.
1
__
3
5
__
6
1
__
3
1
6
1
6
1
6
1
__
2
1
6
1
6
5
The peppers and ham cover __ of the pizza.
6
Adding and Subtracting
5-2 with Unlike Denominators
You can use any common denominator or
the least common denominator to add and
subtract unlike fractions. The least
common denominator (LCD) is the least
common multiple of the denominators.
Adding and Subtracting
5-2 with Unlike Denominators
Additional Example 2A: Adding and Subtracting
Unlike Fractions
Add or subtract. Write each answer in simplest form.
Method 1: Multiplying denominators.
7
3
__
__
–
10
8
7
3
__
– __
10
8
Multiply the denominators. 10 • 8 = 80
56
30
__
– __
80
80
Write equivalent fractions with a common
denominator.
26
__
80
Subtract.
13
__
40
Write the answer in simplest form.
Adding and Subtracting
5-2 with Unlike Denominators
Additional Example 2B: Adding and Subtracting
Unlike Fractions
Add or subtract. Write each answer in simplest form.
Method 2: Use the LCD.
11
3
__ __
– 8
12
11
3
__
__
–
12
8
22
9
__
__
–
24
24
13
__
24
Multiples of 12: 12, 24, …
Multiples of 8: 8, 16, 24, … The LCD is 24.
Write equivalent fractions with a
common denominator.
Subtract.
Adding and Subtracting
5-2 with Unlike Denominators
Additional Example 2C: Adding and Subtracting
Unlike Fractions
Add or subtract. Write each answer in simplest form.
Method 3: Use mental math.
5
1
__
__
+
16
8
5
1
__
+ __
16
8
Think: 16 is a multiple of 8, so the LCD is
16.
5
2
__
__
+
16
16
1
Rewrite __ with a denominator of 16.
7
__
16
8
Add.
Adding and Subtracting
5-2 with Unlike Denominators
Additional Example 2D: Adding and Subtracting
Unlike Fractions
Add or subtract. Write each answer in simplest form.
Method 3: Use mental math.
5
1
__
__
–
16
8
5
1
__
– __
16
8
Think: 16 is a multiple of 8, so the LCD is
16.
5
2
__
– __
16
16
1
__
Rewrite
with a denominator of 16.
8
3
__
16
Subtract.
Adding and Subtracting
5-2 with Unlike Denominators
Check It Out: Example 2A
Add or subtract. Write each answer in simplest form.
Method 1: Multiplying denominators.
8
2
__
– __
10
6
8
2
__
– __
10
6
Multiply the denominators. 10 • 6 = 60
48
20
__
– __
60
60
Write equivalent fractions with a
common denominator.
Subtract.
28
__
60
7
__
15
Write the answer in simplest form.
Adding and Subtracting
5-2 with Unlike Denominators
Check It Out: Example 2B
Add or subtract. Write each answer in simplest form.
Method 2: Use the LCD.
1
4
__
__
–
3
7
4
1
__
– __
7
3
12
7
__
– __
21
21
5
__
21
Multiples of 7: 7, 14, 21, …
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, …
The LCD is 21.
Write equivalent fractions.
Subtract.
Adding and Subtracting
5-2 with Unlike Denominators
Check It Out: Example 2C
Add or subtract. Write each answer in simplest form.
Method 3: Use mental math.
3
1
__
+ __
12
6
3
1
__
+ __
12
6
Think: 12 is a multiple of 6, so the LCD is
12.
3
2
__
__
+
12
12
1
Rewrite __ with a denominator of 12.
5
__
12
6
Add.
Adding and Subtracting
5-2 with Unlike Denominators
Check It Out: Example 2D
Add or subtract. Write each answer in simplest form.
Method 3: Use mental math.
3
1
__
__
–
12
6
3
1
__
__
–
12
6
Think: 12 is a multiple of 6, so the LCD is
12.
3
2
__
__
–
12
12
1
Rewrite __ with a denominator of 12.
1
__
12
6
Subtract.