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5-2 Adding and Subtracting with Unlike Denominators
Warm Up
Lesson Presentation
Problem of the Day
Lesson Quizzes
5-2 Adding and Subtracting with Unlike Denominators
Warm UpAdd. Write each answer in simplest form.
1. + 2. +
3. + 4. +
17__ 1
7__ 8
15__ 3
15__
79__ 2
9__ 11
20__ 4
20__
27__ 11
15__
1 34__
5-2 Adding and Subtracting with Unlike Denominators
Problem of the Day
If it takes 12 minutes to cut a pipe into three pieces, how long would it take to cut the pipe into four pieces?18 minutes
5-2 Adding and Subtracting with Unlike Denominators
Learn to add and subtract fractions with unlike denominators.
5-2 Adding and Subtracting with Unlike Denominators
Vocabulary
least common denominator (LCD)
5-2 Adding and Subtracting with Unlike Denominators
The Pacific Ocean covers of Earth’s surface. The Atlantic
Ocean covers of Earth’s surface. To find the fraction of
Earth’s surface that is covered by both oceans, you can add
and , which are unlike fractions.
1
3__
1
3__
1
5__
1
5__
5-2 Adding and Subtracting with Unlike Denominators
Fractions that represent the same value are equivalent.
Remember!
To add or subtract unlike fractions, first rewrite them as equivalent fractions with a common denominator.
5-2 Adding and Subtracting with Unlike Denominators
Additional Example 1: Cooking Application
Mark made a pizza with pepperoni covering of the
pizza and onions covering another . What fraction of
the pizza is covered by pepperoni and onions?
1
4__
1
3__
1
4__
1
3__
_____+ Find a common denominator for 4 and 3: 4 x 3 = 12.
?
1
4__ 1
3__
1
4__ 1
3__Add + .
5-2 Adding and Subtracting with Unlike Denominators
Additional Example 1 Continued
Write equivalent fractions with 12 as the common denominator.
1
4__
1
3__
_______+
3
12__
4
12__
_____Add the numerators. Keep the common denominator.
1
4__ 1
3__
7
12__
112
112
112
112
112
112
112
The pepperoni and onions cover of the pizza.7
12__
5-2 Adding and Subtracting with Unlike Denominators
Check It Out: Example 1Tori made a pizza with peppers covering of the pizza
and ham covering another . What fraction of the pizza
is covered by ham and peppers?
1
3__
1
2__
1
3__ 1
2__
?1
3__
1
2__
_____+ Find a common denominator for 3 and 2: 3 X 2 = 6.
1
3__ 1
2__Add + .
5-2 Adding and Subtracting with Unlike Denominators
Check It Out: Example 1 Continued
Write equivalent fractions with 6 as the common denominator.
1
3__
1
2__
_______+
2
6__
3
6__
_____Add the numerators. Keep the common denominator.
5
6__
1
3__ 1
2__
16
16
16
16
16
The peppers and ham cover of the pizza.5
6__
5-2 Adding and Subtracting 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.
5-2 Adding and Subtracting 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
10__ 3
8__
–7
10__ 3
8__
–56
80__ 30
80__
Multiply the denominators. 10 • 8 = 80
Write equivalent fractions with a common denominator.
Subtract.
Write the answer in simplest form.
26
80__
13
40__
–
5-2 Adding and Subtracting 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
12__ 3
8__
–11
12__ 3
8__
–22
24__ 9
24__
Multiples of 8: 8, 16, 24, … The LCD is 24.
Write equivalent fractions with a common denominator.
Subtract. 13
24__
Multiples of 12: 12, 24, …
5-2 Adding and Subtracting 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
16__ 1
8__
+5
16__ 1
8__
+5
16__ 2
16__
Think: 16 is a multiple of 8, so the LCD is 16.
Rewrite with a denominator of 16.
Add. 7
16__
1
8__
+
5-2 Adding and Subtracting 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
16__ 1
8__
–5
16__ 1
8__
–5
16__ 2
16__
Think: 16 is a multiple of 8, so the LCD is 16.
Rewrite with a denominator of 16.
Subtract. 3
16__
1
8__
–
5-2 Adding and Subtracting with Unlike Denominators
Check It Out: Example 2A
Add or subtract. Write each answer in simplest form.
Method 1: Multiplying denominators.
– 8
10__ 2
6__
–8
10__ 2
6__
–48
60__ 20
60__
Multiply the denominators. 10 • 6 = 60
Write equivalent fractions with a common denominator.
Subtract.
Write the answer in simplest form.
28
60__
7
15__
5-2 Adding and Subtracting with Unlike Denominators
Check It Out: Example 2B
Add or subtract. Write each answer in simplest form.
Method 2: Use the LCD.
– 4
7__ 1
3__
–4
7__ 1
3__
–12
21__ 7
21__
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, …The LCD is 21.
Write equivalent fractions.
Subtract. 5
21__
Multiples of 7: 7, 14, 21, …
5-2 Adding and Subtracting with Unlike Denominators
Check It Out: Example 2C
Add or subtract. Write each answer in simplest form.
Method 3: Use mental math.
3
12__ 1
6__
+3
12__ 1
6__
+3
12__ 2
12__
Think: 12 is a multiple of 6, so the LCD is 12.
Rewrite with a denominator of 12.
Add. 5
12__
1
6__
+
5-2 Adding and Subtracting with Unlike Denominators
Check It Out: Example 2D
Add or subtract. Write each answer in simplest form.
Method 3: Use mental math.
3
12__ 1
6__
–3
12__ 1
6__
–3
12__ 2
12__
Think: 12 is a multiple of 6, so the LCD is 12.
Rewrite with a denominator of 12.
Subtract. 1
12__
1
6__
–
5-2 Adding and Subtracting with Unlike Denominators
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
5-2 Adding and Subtracting with Unlike Denominators
Lesson Quiz
Add or subtract. Write each answer in simplest form.
1. + 2. –
3. – 4. +
5. Bonnie is making oatmeal bars and the recipes calls for
cup of brown sugar. If she has cup of brown sugar, how
much more does she need?
3
8__ 1
6__ 1
2__ 1
8__
5
12__ 1
6__ 1
6__ 1
8__
3
4__
1
3__
13
24__ 3
8__
1
4__ 7
24__
5
12__ cup
5-2 Adding and Subtracting with Unlike Denominators
1. Add and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-2 Adding and Subtracting with Unlike Denominators
2. Subtract and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-2 Adding and Subtracting with Unlike Denominators
3. Subtract and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-2 Adding and Subtracting with Unlike Denominators
4. Add and identify the answer in simplest form.
A. C.
B. D.
Lesson Quiz for Student Response Systems
5-2 Adding and Subtracting with Unlike Denominators
5. Donna is making tomato soup and the recipe calls for kg of tomato. If she has kg of tomatoes, how much more does she need?
A. C.
B. D.
Lesson Quiz for Student Response Systems
